Design and Analysis of an X-band Phased Array Patch Antenna · The array has achieved a half power...

Design and Analysis of an X-band Phased Array Patch Antenna

Fredrik Gulbrandsen

Electronics Engineering

Supervisor: Egil Eide, IETCo-supervisor: Asgeir Nysæter, FFI

Department of Electronics and Telecommunications

Submission date: June 2013

Norwegian University of Science and Technology

i

Project Description

The goal is to design and analyze an X-band (8-9 GHz) antenna array. The starting point will

be a developed X-band aperture coupled stacked patch antenna element that is to be modified

and used as the antenna element in the array antenna.

Key tasks will be to achieve satisfactory impedance, antenna pattern and polarization over the

desired scan range and frequency bandwidth by including the effect of mutual coupling

between the antenna elements. Other tasks will be to reduce backwards radiation and scan

angles with zero antenna effect due to destructive interference.

The design should be simulated with contacts for connection to a nearby TX/RX module, and

it should be able to handle the temperature rise due to 50 W power amplifiers. The goal is to

arrive at a design that can be demonstrated in a functional model.

If time permits the task also includes testing of the finished antenna in an anechoic chamber

with the reporting of test results and comparisons with and comparisons with simulated

results.

iii

Abstract

An 8x8 array antenna has been designed for a frequency band of 8-8.5 GHz. The design has

been made as a part of a project to develop a digital, active MIMO radar at the Norwegian

Defence Research Establishment (FFI).

The array consists of 64 resonant aperture stacked patch (ASP) antennas. An element spacing

of 16.5 mm ensures that no grating lobes occur over the entire scan range. A scan range of

-55° to 55° and -45° to 45° have been achieved in the E-plane and H- plane respectively. This

scan range was achieved using wide band antenna elements.

Methods to improve the scan range and the reflection coefficient such as electromagnetic

bandgap (EBG) material, defected ground structures (DGS), and adaptive matching circuits

was investigated. All three alternatives were discarded due to either added complexity to the

design or problems incorporating the methods into the design.

The array has achieved a half power beam width of 14° when scanned in broadside direction.

The efficiency of the array is 0.96 which is an important result considering that 50 W is to be

applied to each element.

The antenna element used in the array was based on a design developed during the

specialization project. Measurements on this antenna element were conducted and large

deviations between measured and simulated input impedance were discovered. These

deviations were found to be caused by mechanical properties of the antenna element. The

antenna element was improved and better compliance between measured and simulated

results has been achieved.

v

Sammendrag

Et 8x8 array antenne har blitt designet for et frekvensbånd på 8-8,5 GHz . Designet er utført

som en del av et prosjekt for å utvikle en digital, aktiv MIMO radar på Forsvarets

forskningsinstitutt (FFI).

Arrayet består av 64 resonant aperture stacked patch (ASP) antenner. En element avstand på

16,5 mm sikrer at ingen gitterlober oppstår for skanneområde. En skannområde på -55 ° -55 °

og -45 ° -45 ° er oppnådd i E-planet og H-planet respektivt. Dette skanneområde ble oppnådd

ved hjelp av antenne elementer med et bredt frekvensbånd.

Metoder for å forbedre skanneområde og refleksjon koeffisienten som elektromagnetisk

båndgap (EBG) materialer, defekte jordplan strukturer (DGS), og adaptive matchende kretser

ble undersøkt. Alle tre alternativer ble forkastet på grunn av enten lagt kompleksiteten i

design eller problemer med å gjøre det arbeidet.

Array antennen har oppnådd en half power beam width på 14° i bredside retningen.

Strålingseffektiviteten til matrisen er 0,96, noe som er et viktig resultat tatt i betraktning at 50

W inngangs effekten på hvert element

Antennen element som brukes i arrayet var basert på et design utviklet i løpet av

spesialiseringsprosjektet. Målinger på dette antenne elementet ble gjennomført og store avvik

mellom målt og simulert inngangsimpedans ble oppdaget. Disse avvikene ble funnet å være

forårsaket av de mekaniske egenskapene til antenneelementet. Antenneelementet ble forbedret

og bedre samsvar mellom de målte og simulerte resultater har blitt oppnådd.

vi

Preface

This thesis is submitted in partial fulfillment of the requirements for the degree of master of

science at the Department of Electronics and Telecommunications, Norwegian University of

Science and Technology (NTNU). The work was conducted during the winter and spring of

2013 under the supervision of Egil Eide and was submitted to NTNU June 17th, 2013. The

assignment was given by the Norwegian Defence Research Establishment (FFI) as part of a

project to develop an experimental MIMO radar.

Acknowledgments

First and foremost I want to thank my supervisor at FFI Asgeir Nysæter for the opportunity to

work with this project and for facilitating the work. His help has been invaluable to the

project, he has provided me with all necessary tools and equipment for solving the assignment

and for that I am very grateful.

I also want to thank Yoann Paichard and Karina Vieira Hoel their technical insight has been

very helpful.

Last but not least I want to thank Egil Eide my supervisor at NTNU for coffee and waffles at

meetings, and of course valuable advice on the antenna design and the report.

Trondheim, Norway, June 2013

Fredrik Gulbrandsen

viii

Contents Project Description ...................................................................................................................... i

Abstract ..................................................................................................................................... iii

Sammendrag ............................................................................................................................... v

Preface ....................................................................................................................................... vi

List of figures ............................................................................................................................. x

List of tables ............................................................................................................................ xiv

Acronyms ................................................................................................................................. xv

1 Introduction ......................................................................................................................... 1

1.1 Background .................................................................................................................. 1

2 Theoretical background....................................................................................................... 3

2.1 Array ............................................................................................................................ 3

2.2 Tools .......................................................................................................................... 21

3 The antenna element ......................................................................................................... 23

3.1 Design ........................................................................................................................ 23

3.2 Production .................................................................................................................. 25

3.3 Simulation and measured results ............................................................................... 26

3.4 Analysis of the results ................................................................................................ 31

4 Design of the array ............................................................................................................ 39

4.1 Design procedure ....................................................................................................... 39

4.2 Array design .............................................................................................................. 40

4.3 Mutual coupling ......................................................................................................... 49

4.4 DGS and EBG ........................................................................................................... 49

4.5 Adaptive impedance matching .................................................................................. 52

5 Results ............................................................................................................................... 55

5.1 Array .......................................................................................................................... 55

5.2 The antenna element .................................................................................................. 67

6 Discussion ......................................................................................................................... 75

6.1 Array performance ..................................................................................................... 75

6.2 Radiation .................................................................................................................... 77

6.3 Mutual coupling ......................................................................................................... 79

6.4 Antenna element ........................................................................................................ 80

6.5 Error sources .............................................................................................................. 81

ix

6.6 Future work ................................................................................................................ 81

7 Conclusion ........................................................................................................................ 83

8 Bibliography ..................................................................................................................... 85

Appendix A: Additional theory .............................................................................................. A-1

A.1 Patch antennas ............................................................................................................. A-1

A.2 Antenna parameters ................................................................................................... A-10

A.3 Microwave theory ...................................................................................................... A-14

Appendix B: Measurements ................................................................................................... B-1

B.1 Input impedance ........................................................................................................... B-1

B.2 Radiation patterns ........................................................................................................ B-5

Appendix C: Simulation results ............................................................................................. C-1

C.1 Radiation patterns ........................................................................................................ C-1

Appendix D: Schematic ......................................................................................................... D-1

Appendix E: Derivations ........................................................................................................ E-1

x

List of figures

Figure 1: (a) Linear array. (b) Linear array where the observation point is placed in the far

field. ............................................................................................................................................ 4

Figure 2: Plot of the normalized array factor using different numbers of elements(a), and

different element spacing (b). ..................................................................................................... 6

Figure 3: Array factor of a linear array in end fire mode (a) (b) ............. 8

Figure 4: Effective length of a scanned array............................................................................. 9

Figure 5: (a) Plot of . (b) Half-power beamwidth plotted against scan angle ......... 10

Figure 6: Example of pattern multiplication. (a) Array factor. (b) Element pattern. (c) Total

radiation pattern ........................................................................................................................ 11

Figure 7: General lattice structure [2, p. 19]. ........................................................................... 12

Figure 8: Rectangular array [3, p. 350] .................................................................................... 13

Figure 9: Linear infinite array .................................................................................................. 16

Figure 10: Grounded dielectric slab ......................................................................................... 20

Figure 11: Comparison of HFSS and CST ............................................................................... 21

Figure 12: Side view of the ACSP antenna with ground shield, via cage and RF-transition .. 24

Figure 13: Side view of the production ready antenna ............................................................. 25

Figure 14: Side view of antenna with reference points. ........................................................... 26

Figure 15: The simulated reflection coefficient (S11) for reference point A plotted in a Smith

chart (a) and in dB as a function of frequency (b). .................................................................. 27

Figure 16: The simulated reflection coefficient (S11) for reference point B plotted in a Smith


Figure 17: The measured reflection coefficient (S11) for reference point A plotted in a Smith


Figure 18: Simulated radiation pattern in normalized dB measured at 8.25 GHz in the H-plane

(ϕ=90). ...................................................................................................................................... 30

Figure 19: Measured radiation pattern in normalized dB measured at 8.25 GHz in the H-plane

(ϕ=90). ...................................................................................................................................... 30

Figure 20: The simulated reflection coefficient (S11) of board 1 plotted in a Smith chart (a)

and in dB as a function of frequency (b). ................................................................................. 34

Figure 21: The measured reflection coefficient (S11) of board 1 plotted in a Smith chart (a)

and in dB as a function of frequency (b). ................................................................................. 35

Figure 22: Simulated reflection coefficient of the antenna element with a foam thickness of 3

mm plotted in a Smith chart (a), and in dB as a function of frequency (b). ............................. 36

Figure 23: (a) A view of the three boards. (b) Side view of the modified antenna element. .. 37

Figure 24: The new antenna stack up ....................................................................................... 42

Figure 25: Optimal single element radiation pattern. ............................................................... 43

Figure 26: Normalized gain in dB for an antenna element, E-plane (φ=0°). ........................... 44

xi

Figure 27: Normalized gain in dB for an antenna element placed in an infinite array, E-plane

( ).................................................................................................................................... 45

Figure 28: Front view of the antenna array. ............................................................................. 48

Figure 29: Three different ground defect structures. (a) Dumbbell (b) U-shape (c) back-to-

back U-shape ............................................................................................................................ 50

Figure 30: DGS test bench ....................................................................................................... 50

Figure 31: S21 with DGS and without DGS. ........................................................................... 51

Figure 32: Block diagram of general adaptive impedance matching system ........................... 52

Figure 33: Directional coupler. ................................................................................................ 53

Figure 34: S11 plotted in (a) a Smith chart (b) in dB as a function of frequency. . .... 56

Figure 35: Reflection coefficient at different scan angels (a) E-plane scan ( ) (b) H-

plane scan ( ). ............................................................................................................... 57

Figure 36: Reflection coefficient of different antenna elements for the array in broadside. ... 58

Figure 37: Plot of Floquet modes for (a) 8 GHz, (b) 8.25 GHz, (c) 8.50 GHz. ....................... 59

Figure 38: Polar plot of the normalized antenna gain in dB at 8.25 GHz for (a) the array in

broadside, φ=0°, (b) the array scanned in , , (c) the array scanned in

, , (d) the array scanned in and , .................... 60

Figure 39: (a) Normalized gain for an antenna element placed in an infinite array, φ=0°, (b)

normalized gain for a central antenna element, φ=0°, (c) normalized gain for an edge antenna

element, φ=0°. .......................................................................................................................... 61

Figure 40: Normalized array factor of the array for scan angles (a) broadside, (b)

and (c), and , (d) and .................................. 63

Figure 41: Simulated directivity compared to calculated directivity ....................................... 64

Figure 42: Results from simulations of mutual coupling using element 1 as reference. (a)

Standard array (b) With PEC walls. An element distance of 16.5 mm is used. ....................... 65

Figure 43: Mutual coupling levels in a 2x2 array for different element spacing. .................... 66

Figure 44: Mutual coupling between original antenna elements. (a) E-plane, (b) H-plane.

Element spacing of 50 mm. ...................................................................................................... 66

Figure 45: S11 plotted in (a) a Smith chart (b) in dB as a function of frequency .................... 68

Figure 46: A polar plot of the normalized antenna gain in dB (8.25 GHz), H-plane (ϕ=90°). 68

Figure 47: A polar plot of the normalized antenna gain in dB (8.25 GHz), E-plane (ϕ=0°). .. 69

Figure 48: The measured reflection coefficient (S11) of the modified antenna element plotted

in a Smith chart (a) and in dB as a function of frequency (b). ................................................. 70

Figure 49: Reflection coefficient of the antenna element plotted in a Smith chart for different

distances between the patches. (a) 1.32 mm (b) 1.65 mm (c) 2.02 mm (d) 2.2 mm ................ 71

Figure 50: Reflection coefficient of the antenna element plotted in dB as a function of

frequency for different distances between the patches. (a) 1.32 mm (b) 1.65 mm (c) 2.02 mm

(d) 2.2 mm ................................................................................................................................ 72

Figure 51: Radiation pattern for the modified antenna element at 8.25 GHz in normalized dB,

(a) E-plane, (b) H-plane ........................................................................................................... 73

Figure 52: Cross polarization level of the modified antenna element ...................................... 74

Figure 53: Patch antenna ......................................................................................................... A-1

xii

Figure 54: (a) Microstrip line feed (b) Probe feed (c) Aperture-coupled feed (d) Proximity

feed .......................................................................................................................................... A-2

Figure 55: Reflection coefficient plotted in a Smith chart for (a) Resonant aperture (b) The

ACSP (c) the ASP ................................................................................................................... A-4

Figure 56: The Aperture Coupled Stacked Patch (ACSP) ...................................................... A-5

Figure 57: Reflection coefficient of the ACSP plotted in a Smith chart ................................. A-6

Figure 58: (a) Rectangular slot. (b) Bowtie slot. (C) H-shape slot. (d) Hourglass slot. (e)

Dogbone slot ........................................................................................................................... A-8

Figure 59: Equivalent circuit of an antenna .......................................................................... A-10

Figure 60: Terminated transmission line ............................................................................... A-15

Figure 61: Two port network ................................................................................................ A-16

Figure 62: S11 plotted in a Smith chart for a frequency band of 7-10 GHz (a) Antenna 3, (b)

Antenna 4, (c) Antenna 5 ........................................................................................................ B-1

Figure 63: S11 plotted in dB as a function of frequency (a) Antenna 3, (b) Antenna 4, (c)

Antenna 5 ................................................................................................................................ B-2

Figure 64: S11of the modified antenna element plotted in a Smith chart for a frequency band

of 7-10 GHz (a) Antenna 3, (b) Antenna 4, (c) Antenna 5...................................................... B-3

Figure 65: S11 of the modified antenna element plotted in dB as a function of frequency (a)

Antenna 3, (b) Antenna 4, (c) Antenna 5 ................................................................................ B-4

Figure 66: Anechoic chamber ................................................................................................. B-5

Figure 67: Antenna 4 at 8.25 GHz in normalized dB, (a) E-plane, (b) H-plane ..................... B-6

Figure 68: Antenna 3 at 8.5 GHz in normalized dB, (a) E-plane, (b) H-plane ....................... B-6

Figure 69: Radiation pattern for the Antenna 3 at 8.5 GHz in normalized dB, (a) E-plane, (b)

H-plane .................................................................................................................................... B-7

Figure 70: Cross polarization for antenna 4 at 8.25 GHz ........................................................ B-7

Figure 71: Radiation pattern for antenna 4 at 8.25 GHz in normalized dB, (a) E-plane, (b) H-

plane ........................................................................................................................................ B-8

Figure 72: Radiation pattern for antenna 5 at 8.25 GHz in normalized dB, (a) E-plane, (b) H-

plane ........................................................................................................................................ B-8

Figure 73: Cross polarization of antenna 5 at 8.25 GHz ......................................................... B-9

Figure 74: Rectangular plot of the normalized antenna gain in dB for the array scanned in

(f= 8.25 GHz). Plotted in plane. ................................................................... C-1

Figure 75: Rectangular plot of the normalized antenna gain in dB for the array scanned

in (f= 8.25 GHz). Plotted in φ=0° plane. ................................................................. C-1


in (f= 8.25 GHz). Plotted in φ=0° plane. ................................................................. C-2


in and (f= 8.25 GHz). Plotted in φ=45° plane. ....................................... C-2


in and (f= 8.25 GHz). Plotted in φ=45° plane. ....................................... C-3

Figure 79: Polar plot of the normalized antenna gain in dB for the array scanned in

and (f= 8.25 GHz). Plotted in φ=45° plane. ........................................................... C-3

xiii

Figure 80: Rectangular plot of the normalized antenna gain in dB for an antenna element in an

infinite array environment. φ=0° ............................................................................................. C-4

Figure 81: Rectangular plot of the normalized antenna gain in dB for an antenna element in an

infinite array environment. φ=90° ........................................................................................... C-4

Figure 82: Side view of antenna ............................................................................................. D-2

Figure 83: Schematics of the antenna element ....................................................................... D-3

Figure 84: Cage and RF-Transition. Red vias go from ground shield to feed layer. White vias

go from ground shield to ground plane .................................................................................. D-4

Figure 85: Schematic of the array .......................................................................................... D-5

xiv

List of tables

Table 1: Properties of Rogers XT/duroid 6035 HTC, Rogers RT/duroid 5880 and Rohacell 71

IG .............................................................................................................................................. 24

Table 2: Measured antenna dimensions and corresponding dimensions of the antenna model.

.................................................................................................................................................. 32

Table 3: Specifications ............................................................................................................. 39

Table 4: Bonding materials ...................................................................................................... 48

Table 5: Simulation results for array ........................................................................................ 58

Table 6: Simulated radiation pattern properties ....................................................................... 62

Table 7: Radiation properties for array factor .......................................................................... 62

Table 8. Calculated results ....................................................................................................... 64

Table 9: Simulation results for the modified antenna element ................................................. 67

Table 10: Values for the schematic ........................................................................................ D-1

xv

Acronyms

ACSP - Aperture- Coupled Stacked Patch antenna

ASP - resonant Aperture Stacked Patch antenna

DGS - Defected Ground Structure

EBG - Electromagnetic BandGap

HPBW - Half-Power BeamWidth

MIMO - Multiple Input Multiple Output

PA - Power Amplifier

TE- Transverse Electric

TEM - Transverse ElectroMagnetic

TM- Transverse Magnetic

VSWR - Voltage Standing Wave Ratio

1

1 Introduction

This report presents the design and analysis of an X-band 8x8 phased array patch antenna.

The antenna will be used in an active radar system for experimenting with MIMO algorithms.

The antenna is designed to have a center frequency of 8.25 GHz and a frequency band of 8-

8.50 GHz. The work presented here is the continuation of last fall's specialization project

where an aperture-coupled stacked patch antenna was designed. This antenna has been used

as a building block for the array antenna.

The report consists of seven chapters. After the introduction the necessary theoretical

background is presented. Then a chapter describing the antenna element follows, including a

short summary of the design, and a comparison between measured and simulated results. The

design of the array and all the steps and choices made are thoroughly explained in chapter

four. Important results are presented in chapter five, and then discussed in the next chapter. In

the end the conclusion follows.

1.1 Background

Today radar systems are used in many different applications, from large military systems

which are used to detect ballistic missiles, to smaller commercial systems as car radars. To

increase the range of possible applications much emphasis is put on developing cheap and

compact radar systems. In many applications it is desirable to use phased array antennas, this

often leads to expensive and large radar systems which limits the possible applications.

However, the development of patch antennas has enabled cheap, lightweight, and compact

phased array antennas. Combining patch arrays with new semiconductor circuits it is now

possible to make cheaper and more compact radar systems.

Work is constantly being done to discover new ways of improving radar performance.

Recently it has been discovered that use of Multiple Input Multiple Output (MIMO)

techniques have the potential to enhance radar performance. MIMO techniques was originally

developed for wireless communication systems to increase capacity. Development of a

MIMO radar is currently being conducted at FFI (Forsvarets Forskningsinstitutt). The goal is

to build an active radar system with a phased array antenna to test MIMO algorithms. This

report presents the design of the phased array antenna.

A project goal has been to build a cheap and compact 8x8 array using patch antenna elements.

The array should be designed for a frequency band of 8-8.5 GHz and should be linearly

polarized. Goals during the antenna development have been to achieve a high scan range, a

high radiation efficiency and a low reflection coefficient. Each antenna element need to

handle up to 50 W of input power and the system impedance is 50 .

2

The antenna element used in the array was developed in the specialization project last fall [1].

An aperture-coupled stacked patch antenna was designed with a frequency band of 8-8.5

GHz. It has been produced and measured results are presented later in the report.

3

2 Theoretical background

This chapter presents the most important theoretical background used in the design of the

array. This project is based on work done in the specialization project conducted last fall

(2012), this work is described in [1]. Topics such as antenna parameters, microwave theory

and patch antennas are presented in [1]. These topics are of importance for this project as

well, but to keep the page number down and the focus on array antennas it was chosen to put

these topics in Appendix A.

2.1 Array

An array antenna consists of multiple antenna elements which are grouped together to form

one antenna. Grouping antenna elements together results in several advantageous properties

such as; higher directivity compared to a single antenna element, it enables electronic steering

of the beam, and control over the radiation pattern (i.e. control over side lobe levels, and null

points). These properties are mainly due to the positive and negative interference that occur

when the fields from each antenna elements combine. The antenna elements need not be

identical, but identical antenna elements makes the analysis easier and is more practical in

most applications. The radiation properties of an array antenna are controlled by the antenna

element, the geometry of the array, and the amplitude and phase of the excitation of each

element.

In this section two different ways of modeling arrays are presented and compared; first the

classic approach, then an approach using Floquet analysis. Important topics such as mutual

coupling, scanning, scan blindness and grating lobes are also discussed.

2.1.1 Classic array analysis

Classic array analysis uses the superposition principle where the total field is obtained by

vector adding the fields produced by each antenna element. Figure 1(a) shows a linear array

of N identical elements. The radiated electrical field from a single element at an observation

point can be expressed as [2, p. 2]

(2.1)

4

where A is the amplitude of the input excitation, is the distance from the antenna element to

the observation point and is the element pattern.

Figure 1: (a) Linear array. (b) Linear array where the observation point is placed in the far field.

The total field of the array is the vector sum of the fields from the antenna elements

(2.2)

Here is the phase difference between elements. Assuming the observation point is located in

the far-field, several simplifications can be made as shown in Figure 1(b). Mathematically the

simplifications are

for phase variations

for amplitude variations

(2.3)

where d is the element spacing. A looser approximation of can be used for the amplitude

term since changes slowly. For the phase term a much stricter approximation must be

used since changes rapidly. Inserting these approximations into (2.2) gives

5

(2.4)

which can be written as

(2.5)

This expression can be divided into two parts

(2.6)

where is the field produced by a single element as given in (2.1), and AF is the array

factor depending on the geometry of the array, and amplitude and phase difference of the

excitation.

(2.7)

(2.6) is called pattern multiplication and is valid when the array consists of identical elements.

This analysis has not taken into account mutual coupling between elements. Mutual coupling

will lead to different element patterns for each element and therefore the pattern

multiplication is not valid.

2.1.1.1 Array factor

To get a deeper understanding of the array factor equation (2.7) is applied to a linear uniform

array1 located on the x-axis. The array factor can then be written as

(2.8)

1 Same spacing and amplitude of excitation.

2 Software used in the design.

6

which again can be written as [3, p. 294]

(2.9)

where

(2.10)

Equation (2.9) is the normalized array factor of a linear array located on the x-axis. Figure 2

shows (2.9) for various values of N and d. It should be noted that a larger N gives a narrower

major lobe. A larger element spacing will also give a narrower major lobe. This means that

the directivity of an array can be increased by either increasing the number of elements or the

element spacing. It is also seen that increasing N gives a lower side lobe level.

Figure 2: Plot of the normalized array factor using different numbers of elements(a), and different

element spacing (b).

Because of the periodic nature of the sine function, equation (2.9) has an infinite number of

maxima. These are found using

(2.11)

and they are located at

7

(2.12)

The first maximum is called the major lobe and occurs when

(2.13)

The other maxima are called grating lobes. Grating lobes are unwanted in most applications

since they transmit and receive energy in unwanted directions. Grating lobes occur when the

spacing between elements are large enough to permit in-phase addition of radiated fields in

more than one direction [3, p. 352]. To avoid grating lobes the array should be designed so

that . Solving with respect to d gives

(2.14)

where . is the largest phase difference and is found using (2.16). Inserting

(2.16) into (2.14) gives

(2.15)

is chosen so that is minimized, this is the angle where the first grating lobe will

occur. is the scan angle that maximizes . The largest value the denominator of

equation (2.15) can achieve is 2, this happens when . Making the element

spacing less than will therefore ensure that no grating lobes occur for any scan angle.

Equation (2.15) can be used to optimize the element spacing for a given scan angle.

2.1.1.2 Scanning

By varying in (2.13) the direction of the major lobe can be steered. This is called phase

steering and is widely used in many applications such as radar and communication systems. It

makes it possible to change the direction of the major lobe without moving the antenna

mechanically. To determine what phase difference to use for a wanted scan angle (2.13) is

solved with respect to

(2.16)

For a scan range of 0°-180°, has to vary from to .

When the major lobe is pointed in a direction that is perpendicular to the array it is called a

broadside array, is needed to achieve this. When the major lobe is pointed in a

8

direction that is parallel to the array it is called an end fire array, is needed to

achieve this. The radiation pattern of an end fire array is shown in Figure 3(a).

To avoid grating lobes when scanning an array, equation (2.15) can be used. It gives an upper

limit on the element spacing. Choosing the element spacing just smaller than will ensure

that the grating lobe will not reach maximum strength, but a large lobe will still be present.

This can be seen in Figure 3(b), where the array factor of a linear array in end fire mode is

plotted. The element spacing is . It is observed that a large part of the grating lobe is

still present. To further reduce this lobe the element spacing should be decreased.

Figure 3: Array factor of a linear array in end fire mode (a) (b)

When scanning an array a phenomenon called beam broadening will occur. An array has the

narrowest main beam at broadside, but the main beam will broaden when scanned away from

broadside. This can be seen from the directivity equation for a broadside array [3, p. 315]

(2.17)

is the maximum directivity of the array, which is an indication on the width of the main

beam, and L is the total length of the array. As seen in Figure 4 the effective length of the

array will be reduced when the beam is scanned away from broadside. Effective length is

defined as the length of the array seen from the observation point.

9

Figure 4: Effective length of a scanned array.

The effective length is given by

(2.18)

To determine the beam broadening factor, the directivity for a variable scan angle is

divided by the maximum directivity.

(2.19)

The last step can be done if . Equation (2.19) says that the maximum directivity of an

array at any scan angle is the maximum directivity of an array in broadside reduced by a

factor of , or mathematically

(2.20)

where is given by equation (2.17). This is a crude first order approximation of the beam

broadening effect, but it illustrates the point.

A more precise model of the beam broadening is given in [3, p. 304]. Here the half-power

beamwidth is given as a function of scan angle

10

(2.21)

Equation (2.21) is accurate around broadside and becomes less accurate for scan angles closer

to end fire.

To compare these two methods both equation (2.20) and (2.21) are plotted in Figure 5.

Figure 5: (a) Plot of . (b) Half-power beamwidth plotted against scan angle

When comparing the two plots in Figure 5 one has to remember that the directivity and the

half-power beamwidth has opposite characteristics (when the directivity increases the HPBW

decreases). When doing that it is clear that the two models have similar but inverse

characteristics.

Beam broadening is a limiting factor in phase-steered array antennas being used in radar

applications. The reason for this is that the angular resolution of a radar is determined by the

half-power beamwidth [3, p. 43]. A large beamwidth gives a low angular resolution. The

beamwidth will increase as the beam is scanned away from broadside, thus lowering the

angular resolution. In order to satisfy the angular resolution requirement, the array should be

designed so that the specified angular resolution are met at the maximum scan angle.

It is not only the array factor that determines the performance of the scanning array. It is clear

from pattern multiplication that the element pattern will equally affect the total radiation

11

pattern of the array. It is therefore important to consider the element pattern when designing

an array. Figure 6 shows the effect of the element pattern on the total radiation pattern.

Figure 6: Example of pattern multiplication. (a) Array factor. (b) Element pattern. (c) Total radiation

pattern

The element pattern will introduce scan loss. This occurs when the gain of the antenna

element is not constant over the entire scan range. This leads to a main beam with different

gain for different scan angles. Scan loss is given as [2, p. 13]

(2.22)

where G is the gain of the antenna element, is the maximum gain, and is a specific

direction. An element often has the highest gain in the broadside direction and then the gain

12

decreases to the sides. If the gain decreases rapidly the main beam will be severely attenuated

when scanned off broadside. If the main beam of the array factor was scanned towards 60°

instead of 0° in Figure 6, it would be damped by the element pattern. So an optimal element

pattern for scanning applications is constant over the entire scan range. This means that the

major lobe of the array factor is affected equally over the entire scan range.

The scan loss property is not only negative. An element pattern with near constant gain over

the entire scan range and then rapidly decreasing gain will not affect the major lobe but will

decrease the side lobes and backwards radiation. This is seen in Figure 6 where the element

pattern completely removes the backwards radiation.

2.1.1.3 Planar array

The planar array is a two dimensional structure, unlike the linear array which is one

dimensional. This extra dimension gives the planar array several advantageous properties. The

main beam can be steered in any direction, it has a more symmetrical pattern and lower side

lobe levels [3, p. 349]. The planar array can have many different lattice structures. A general

lattice structure is shown in Figure 7. Here and are the length and height of the unit

cell, and is the unit cell angle. Together these parameters describe the lattice structure.

Figure 7: General lattice structure [2, p. 19].

A common lattice structure is the rectangular grid, in this case . This makes and

the element spacing. Figure 8 shows the geometry of a rectangular array in the x-y plane.

If identical antenna elements are used, then pattern multiplication will apply.

13

Figure 8: Rectangular array [3, p. 350]

The rectangular array can be seen as multiple linear arrays lined up besides each other. The

array factor is therefore given as [3, p. 351]

(2.23)

Here and represents the amplitudes, and and is the phase difference between

elements in x and y direction respectively. From equation (2.23) it can be seen that the array

factor of a rectangular array is the product of the array factors of a linear array in x and y-

direction.

(2.24)

Assuming uniform amplitude the normalized array factor can be written as [3, p. 351]

(2.25)

where M is the number of elements in x-direction and N is the number of elements in y-

direction.

14

(2.26)

The maxima of each factor of (2.25) are given as

n (2.27)

As for the linear array the first maximum is the major lobe and the other maxima are grating

lobes. To locate grating lobes the equations under can be used [3, pp. 352-353]

(2.28)

and

(2.29)

For a grating lobe to exist both forms of (2.29) must give the same value. Since the array

factor of a rectangular array is given by the product of array factors for linear arrays in x and

y-direction, a relationship between equation (2.15) and equations (2.28) and (2.29) is

expected. This is confirmed by applying equations (2.28) and (2.29) on a linear array in x-

direction ( , , m=1, and n=0). This results in

(2.30)

which gives

(2.31)

This is the same equation as (2.15). The first grating lobes of a rectangular array will occur

either at ( , ) or depending on the scan angle. (2.15)

can therefore be used to determine the maximum element spacing for rectangular arrays. To

avoid grating lobes make and [3, p. 352].

As for a linear array the rectangular array can be phase-steered. The difference is that the

main beam of the rectangular array can be pointed in any direction. Scanning is done by

controlling the phase difference between elements in both x and y-direction. From (2.27) the

and can be determined for a given scan angle ( )

15

(2.32)

The half-power beamwidth of a large rectangular array near broadside is approximately by [3,

p. 357]

(2.33)

Here and are the half-power beamwidths of broadside linear arrays in x and y-

direction respectively and can be determined using equation (2.21). For equation

(2.33) reduces to

(2.34)

The half-power beamwidth increases with a factor of when scanned away from

broadside. This result supports the beam broadening factor that was derived earlier in the

chapter.

2.1.2 Floquet analysis

[2, pp. 61-154]

Another and relatively new method of analyzing arrays is the Floquet modal based approach.

A brief overview of this approach is given here since HFSS2 uses Floquet analysis to simulate

arrays. It is also of interest to compare the results from the classical approach to results from

the Floquet modal based approach. Floquet analysis has some advantages over the classical

approach. These advantages are that it considers the effect of mutual coupling on both the

input impedance of the antenna elements and the element pattern, and it models scan

blindness. Even though the two approaches are very different it will be shown that results

obtained by the classical approach is recreated by Floquet analysis.

Floquet analysis works only for infinite arrays. For this reason the accuracy of the method

when analyzing a finite array can be doubted, but [2] shows that the performance of a finite

array can be determined accurately using infinite array results. This is done by exciting only a

finite amount of elements in the infinite array and leaving the other elements unexcited when

analyzing the array. This gives a good approximation of a finite array. Another reason why

accurate results can be expected is that central elements in a relatively large array experiences

2 Software used in the design.

16

approximately the same mutual coupling as elements in an infinite array. This means that their

input impedance and element radiation pattern are similar.

The basis of Floquet analysis for arrays is the Floquet series. It is similar to a Fourier series

except for an additional periodicity in phase. A function with both periodic magnitude and

phase but with different periodicities is given as [2, p. 65]

(2.35)

is a complex function and is a real constant. This function has a periodicity of , and

the phase of decreases by every interval . Doing a Floquet series expansion on

(2.35) gives [2, p. 66]

(2.36)

where is the Fourier transform of , is the spectral frequency.

How these equations can be used to model an array is presented below.

Figure 9 shows a linear infinite array of y-directed uniform current sources, the current

sources are surface currents so z=0. The current excitation function is given as [2, p. 70]

(2.37)

where is the element spacing and is the phase difference between the elements. The

current excitation function is more or less identical to equation (2.35), so a Floquet series

expansion can be used to describe the electromagnetic fields produced by this array. When

sources can be described by functions of the same form as equation (2.35) they are called

Floquet sources.

Figure 9: Linear infinite array

17

The electromagnetic field components produced by the current sources are given by [4, p.

601]

(2.38)

and are permittivity and permeability, respectively. is a vector potential and needs to be

determined before the electric and magnetic fields can be found. The vector potential is

determined by using the inhomogeneous Helmoltz equation [4, p. 339]

(2.39)

where is the current density and is the free space wave number. Since the current sources

are y-directed , equation (2.39) can then be written in scalar form as

(2.40)

The current sources lies on the surface and therefore can be expressed by [2, p. 71]

(2.41)

is the Dirac delta function and it ensures that the current density is zero for . Doing

a Floquet series expansion on the right side of (2.41) and inserting into (2.40) gives

(2.42)

A solution for is given by [2, p. 72]

(2.43)

18

where

(2.44)

Using (2.38) the electric field is found to be [2, p. 71]

(2.45)

were the time factor is added. The exponential term in (2.45) is a Floquet mode.

Comparing (2.45) with the equation below will help interpret the result.

(2.46)

This equation represents a plane wave propagating in z-direction, it is polarized in x-direction

and has an amplitude of [4, p. 356]. The similarities in the exponential terms of (2.45) and

(2.46) leads to the conclusion that each Floquet mode represents a plane wave and that the

total electric field is the summation of all these plane waves. Each mode has its own

propagation direction relative to the z-axis which is given by [2, p. 72]

(2.47)

This equation can be simplified to (see Appendix E)

(2.48)

This is the same equation as (2.12), which gives the direction of every maxima of (2.9). This

means that the Floquet modes propagates in the same direction as the maxima of (2.35). The

n=0 Floquet mode is the main beam and the other modes represent grating lobes. For a

19

Floquet mode to become a propagating grating lobe has to be real, if not it is a evanescent

Floquet mode and does not propagate. For to be real

(2.49)

This equation can be used to find the maximum element spacing of the array to avoid grating

lobes. From equation (2.48) the phase difference for a given scan angle can be

determined, this is then inserted into equation (2.49), which gives

(2.50)

Solving with respect to gives

(2.51)

where . This equation is the same as (2.15). The results obtained in (2.48) and

(2.51) shows that both approaches produces same results.

2.1.2.1 Scan blindness

Scan blindness occurs when the reflection coefficient approaches unity for a given scan angle.

This means that the array reflects all the incoming energy, and will therefore not radiate. For

patch array scan blindness is mainly caused by surface waves [3, p. 866]. Scan blindness is

detrimental to the scan performance of the array and needs to be accounted for. One

advantage of Floquet analysis is that scan blindness can be analyzed.

In Floquet analysis scan blindness occurs when the propagation constant of a guided mode

coincides with that of a Floquet mode. The modes will couple strongly which leads to a

resonance and all the energy will then be reflected back into the circuit [2, p. 79]. For a patch

array the guided mode will be surface waves excited by each patch.

2.1.3 Mutual coupling

Mutual coupling is an important phenomenon and needs to be taken into account when

designing arrays. When antenna elements are put in proximity of each other, like in an array,

their fields will couple together and change the antenna element properties. Mutual coupling

will affect the input impedance of the elements and the elements radiation patterns [3, p. 468].

Parameters controlling the level of mutual coupling are; the element spacing, the relative

placement and the radiation pattern of the elements [3, p. 478].

20

To explain the basic mechanisms of mutual coupling a simple example is presented. Two

antennas are placed in the vicinity of each other. Only one antenna is excited and therefore

radiates. Some of the energy will reach the second antenna and excite a current. The second

antenna will then start to radiate, and some of the energy will reach the first antenna. This will

alter the current distribution on the first antenna and therefore alter its input impedance. In

summary, an antenna placed in vicinity of another object will experience a change in the

current distribution which leads to a change in input impedance.

In an array the mutual coupling can be caused by several types of fields. For patch arrays the

mutual coupling is mainly caused by; space waves which has a radial variation of , higher

order waves which has a radial variation of , and surface waves with a radial variation of

. Because of different radial variation terms, each field will dominate the mutual

coupling at different separations. Space waves and higher order waves will dominate at small

separations while the surface waves will dominate at larger separations [3, pp. 857-858].

In patch antennas a large part of the mutual coupling is caused by surface waves. They travel

along interfaces between media with different dielectric constants.

Figure 10: Grounded dielectric slab

When moving away from the interface between two media, the surface waves decay

exponentially. Both TM3 and TE

4 modes can exist. The TM0 mode is the fundamental mode

and has zero cut-off frequency. The cut-off frequency of a TMn mode traveling on a grounded

dielectric slab is given by [5, p. 137]

(2.52)

where d is the height of the dielectric slab, is the dielectric constant and c is the velocity of

light in vacuum. From this equation one can see that to minimize the number of TM modes

excited one has to make the dielectric layer thin and keep the dielectric constant low. The

same is true for TE modes.

3In a TM mode the magnetic field components are transverse to the propagation direction

4 In a TE mode the electric field components are transverse to the propagation direction

21

In rectangular patch arrays the level of coupling between elements is dependent on the

relative placement of the elements. The reason for this is that the dominant surface wave

mode is the TM0 and that mode couples more strongly in the E-plane direction [3, p. 858].

The input impedance of an array will change as a function of scan angle because the mutual

coupling between the elements change for different scan angles.

2.2 Tools

2.2.1 HFSS

HFSS is a 3D full wave electromagnetic field simulator. It uses the finite element method

together with adaptive meshing to solve the wave equations. If a 3D model has been made

HFSS sets up the mesh automatically. HFSS computes S-parameters, it can calculate and plot

both the near and far field radiation and compute important antenna parameters such as gain

and radiation efficiency.

To verify the accuracy of HFSS an antenna has been simulated in both HFSS and a similar

software package called CST. The results are shown in Figure 11.

Figure 11: Comparison of HFSS and CST

The results are relatively similar, which is a good indication that HFSS has the required

accuracy.

22

2.2.1.1 Array simulation

HFSS has three standard methods for modeling and simulating arrays; the Finite Array

method, the Finite Array domain decomposition (DDM), and the unit-cell with Floquet ports.

The first method, the Finite Array method is the straight forward approach to model and

simulate an array. Here the entire array is modeled in HFSS with each antenna element having

its own excitation. This is the most accurate method, but it demands large amounts of memory

and it is very time consuming. It is therefore not an efficient method to use when tuning an

array.

The second method, the Finite Array DDM is an accurate method including mutual coupling

between elements and edge effects5. This method is almost as accurate as the first method but

demands less memory and are faster. This method uses two techniques to decrease solving

time and memory use. The first technique is the domain decomposition (DDM). It divides the

array into smaller parts and solves each part on different computers. This reduces the

simulation time. The second technique is the use of a unit cell. The simulator will use the

mesh obtained when simulating the unit cell on all the antenna elements in the array. This

saves time and memory since the meshing procedure is both time consuming and memory

demanding. Even though this method is far more efficient than the first method it is still too

slow for tuning an array.

The third method uses the unit cell and Floquet ports. The Floquet port enables HFSS to do a

Floquet analysis as described in the theory chapter. This means that the array is approximated

as an infinite array and edge effects are therefore ignored. However it does take into account

mutual coupling between elements. This method will give accurate results for antenna

elements in the middle of the array and the larger the array is the more accurate the method

becomes. This is due to the infinite array approximation. The solving time is highly reduced

and much less memory is needed, since only the unit cell is simulated. This method is

therefore the best one for tuning an array.

5 Antenna elements on the edge will have different properties from elements placed in the middle.

23

3 The antenna element

The design of the antenna element was done in the specialization project and is described in

detail in [1]. A short summary of the design is presented here. Measured results are presented

and compared to the simulated results. It is recommended to read Appendix A.1 before

reading this chapter if one is not familiar with patch antennas.

3.1 Design

The design was based on the basic patch antenna. This was done for several reasons; it is a

well known technology widely used in many applications, it is relatively cheap and easy to

manufacture, it also enables the mounting of electronic components on the back side, but most

important the patch antenna enables design of compact and lightweight arrays.

Four different methods for feeding the patch antenna were considered; the microstrip line

feed, probe feed, aperture-coupled feed, and proximity feed. The aperture-coupled feed was

chosen due to a better fit for this application. It gives low cross polarization, low spurious

feed radiation and it is beneficial that the antenna can be fed from the backside when

implementing an array.

The required frequency band of the antenna is 8-8.50 GHz with a center frequency of 8.25

GHz. For a patch antenna the biggest limitation on the bandwidth is the input impedance. A

low reflection coefficient over the frequency band is necessary because of the large amount of

power delivered by the power amplifier (PA). Three techniques for increasing the bandwidth

and improving the reflection coefficient was considered; resonant aperture, aperture-coupled

stacked patch (ACSP) and resonant aperture stacked patch (ASP). The ACSP was chosen

because it has lower backwards radiation than the other two alternatives considered. Low

backwards radiation is important for this application because of the electronic components on

the backside of the antenna, and more power directed forward gives a longer radar range.

The materials used are important both for the electronic and thermal properties of the antenna.

A Hi-Lo dielectric constant configuration has been used [6]. The lower patch is etched on a

substrate with a high dielectric constant and the upper patch is etched on a substrate with

lower dielectric constant. This reduces the surface wave loss, decrease cross-polarization, and

further increase the bandwidth of the antenna.

For the lower layers of the antenna the Rogers XT/duroid 6035HTC was chosen. This

substrate has a low loss tangent and high thermal conductivity minimizing the temperature

rise in the antenna. A foam type substrate was chosen for the upper layer to obtain a low

dielectric constant. The material used is Rohacell 71 IG. The upper patch is etched on a thin

layer of Rogers RT/duroid 5880 which is placed on top of the foam substrate. This is done

since etching of copper is not possible on the Rohacell 71 IG. The properties of the materials

used are listed in the Table 1

24

Table 1: Properties of Rogers XT/duroid 6035 HTC, Rogers RT/duroid 5880 and Rohacell 71 IG

Parameter 6035HTC 5880 71 IG Units

Dielectric constant 3.6 2.2 1.09

Loss tangent 0.0013 0.0009 0.0034

Thermal conductivity 1.44 0.20 W/m/K

Thermal coefficient of

-66 -125 Ppm/C

The two patches were made rectangular to reduce cross polarization. The feed line was

designed to have a characteristic impedance of 50 . For increased level of coupling and

reduced backwards radiation a H-shape slot was used.

A ground shield was added behind the slot to reduce the backward radiation and to increase

the area where the electronic components can be placed. The slot is surrounded by tightly

spaced vias which connects the two ground planes. The vias form a cage reducing the

excitation of waves that can travel through the substrate.

Figure 12: Side view of the ACSP antenna with ground shield, via cage and RF-transition

Since the feed and component layers are separated by the ground shield a RF-transition has

been made. This structure is designed to transfer the RF signal from the component layer to

the feed layer without any leakage. It consists of a center via that connects the two layers

through a hole in the ground shield. The center via is surrounded by other vias. They work as

the outer conductor of a coaxial cable and holds the fields inside the structure so that leakage

is minimized.

No mathematical model of this antenna was found but guidelines [7] [8] and design examples

[9] [10] exist. These guidelines and design examples were used together with HFSS to design

the antenna in a step by step process. The slot size, patch sizes, and substrate thicknesses were

adjusted to achieve the wanted properties.

25

3.2 Production

The antenna shown in Figure 12 is a complicated construction. It consists of six copper layers,

both blind6 and buried

7 vias and three different substrate types. This makes the production

expensive and technically difficult, and therefore, additional steps was done to make the

antenna ready for production. The final stack up can be seen in Figure 13.

Because of the foam substrate the antenna had to be produced in three parts and assembled

using plastic screws8. The number of via types was reduced by redesigning the RF-transition

as can be seen in Figure 13. A surface mounted SMA connector was placed on the component

layer to enable antenna measurements.

Figure 13: Side view of the production ready antenna

6 A via that starts at a outer layer and ends in a middle layer.

7 A via that starts and ends in middle layers.

8 No bonding material was found that could be used without deforming the foam substrate.

26

3.3 Simulation and measured results

For simulation or measurement of the antenna input impedance a reference point is needed.

The reference point used when tuning the antenna in HFSS is shown in Figure 14 (point A). It

was placed at this position to ensure a good match for the power amplifier, since the PA was

to be placed in this area. The simulated results using A as the reference point are shown in

Figure 15. Measuring the input impedance directly at this point is difficult so a SMA

connector was added. To ensure good compliance between measured results and simulated

results it was necessary to use the same reference point for both simulation and

measurements. Two alternatives could be used to achieve this; a SMA connector could be

included in the model, or the connector could be calibrated away during measurements, this

would move the reference point from B to A. The first alternative was chosen since the latter

alternative are less accurate owing to the abrupt transition from the coax connector to the

microstrip line.

Figure 14: Side view of antenna with reference points.

A SMA connector was modeled in HFSS and new simulations were conducted with the

reference point moved to point B. The results are shown in Figure 16. As expected the input

impedance of the antenna has changed after moving the reference point. The two main

reasons for the change are the adding of the transmission line and the transition from coax to

microstrip line. When adding length to a transmission line the change in input impedance can

be predicted by using the following equation [5, p. 59].

27

(3.1)

Here is the characteristic impedance of the transmission line, and is the load impedance,

which in this case is the input impedance of the antenna at reference point A. is the

additional length of transmission line and is the phase constant. In this case equation (3.1)

would not give an accurate prediction since the transition from coax to microstrip line also

affects the result.

Figure 15: The simulated reflection coefficient (S11) for reference point A plotted in a Smith chart (a) and

in dB as a function of frequency (b).

28

Figure 16: The simulated reflection coefficient (S11) for reference point B plotted in a Smith chart (a) and


A network analyzer was used to measure the input impedance of the antenna. After calibration

the reference point for the measurement was located at point B. So identical reference points

for measurement and simulation were obtained and therefore similar results were expected.

The measurement results are shown in Figure 17.

29

Figure 17: The measured reflection coefficient (S11) for reference point A plotted in a Smith chart (a) and


To measure the radiation pattern the new antenna hall at NTNU was used. The antenna was

placed in an anechoic chamber across from a reference antenna. Then the radiation pattern

was measured by rotating the antenna and exciting the reference antenna. Simulated and

measured results are presented in Figure 18 and Figure 19. A description of the measurements

and more results can be found in Appendix B.

30

Figure 18: Simulated radiation pattern in normalized dB measured at 8.25 GHz in the H-plane (ϕ=90).

Figure 19: Measured radiation pattern in normalized dB measured at 8.25 GHz in the H-plane (ϕ=90).

31

3.4 Analysis of the results

3.4.1 Input impedance

As seen from the results presented in the section above (Figure 16 and Figure 17) there were

large deviations between the measured and simulated input impedance. This presented a

severe problem that had to be solved. One important reason for producing the antenna

elements was to test the accuracy of HFSS. It is difficult to tune the array using HFSS if not

better compliance between simulation and measured results can be achieved. Several possible

reasons for these deviations were investigated.

Inaccuracies in the simulator.

Bad simulation setup.

Measurement errors

Production errors.

Bad modeling of the SMA connector.

HFSS is a commercial software used by many antenna developers. It is therefore unlikely that

inaccuracies in the simulator causes such large deviations as experienced in this case. Also

results from [9] show that HFSS can produce simulation results giving good compliance with

measured results.

To eliminate the possibility of a bad simulation setup an expert from ANSYS9 was consulted.

The simulation setup was inspected and improved. The improvements led only to small

changes in the simulation results. It was therefore concluded that the simulation setup was not

the reason for the large deviations.

Five antennas were produced and measurements of their input impedance were performed.

Only small deviations between the antenna input impedances were observed. To decrease the

probability of measurement errors two different network analyzers were used and all the

measurements were performed three times on different occasions. The difference in results

between the two network analyzers were negligible. It was also negligible differences

between the three measurements. Since no large deviations occurred between the different

measurements it was concluded that it is unlikely that measurement errors were the reason for

the large deviations.

The next error source investigated was production errors. This was the most likely cause of

error because of the complicated structure of the antenna. In this report production errors are

used as a collective term for all error sources that causes differences between the

manufactured antenna and the antenna model10

. Production errors occur during the

manufacturing process and can for example be differences in dimensions owing to process

variations, it can be caused by use of wrong materials, or it can be due to incorrect thickness

9 The company that makes HFSS.

10 The simulated antenna.

32

of a substrate layer. These differences will of course lead to deviations between measured and

simulated results.

Process variations is random variations in the process that every fabrication process suffers

from. It will lead to differences between the manufactured antenna and the simulated antenna,

but most importantly it will lead to differences between each antenna element. When

measuring the input impedance of each antenna only small differences in results were

observed. This is a strong indication that the process variations are small and therefore not the

reason for the large deviations between measured and simulated results.

In cooperation with the manufacturer several errors were discovered. First a different bonding

material than ordered was used. The bonding material had a different dielectric constant, but

because the bonding material is thin only small changes in the input impedance were

expected. Simulations confirmed this. The gerber files11

had been converted from millimeters

to inches, introducing small errors. Simulations showed that these errors were too small to

affect the results noticeably.

To verify the antenna dimensions a digital caliper was used for measurements of the antenna

dimensions. The results are listed in Table 2.

Table 2: Measured antenna dimensions and corresponding dimensions of the antenna model.

Antenna 2 Antenna 3 Antenna 4 Antenna 5

Antenna

model

Total thickness

(mm) 7.12 7.10 7.10 7.10 7.03

Thickness of

board 1(mm) - 4.58 4.58 4.58 5.6

Thickness of

board 2 (mm) - 2.42 2.43 2.42 2.3

Patch 1 (mm) - 10.5x8 10.48x8 10.49x7.97 10.5x8

Patch 2 (mm) - 13.23x11.5 13.33x11.48 13.23x11.5 13.3x11.5

The measurements showed that board 2, which is the foam layer, was thicker for the

manufactured antennas than for the antenna model. The thickness of the foam layer

determines the level of coupling between the two patches and are therefore a crucial

parameter. A difference of 0.1 mm would lead to observable change in input impedance.

Simulations done with a foam thickness of 2.4 mm confirmed this. Simulations showed also

that the 0.1 mm difference in foam thickness was not solely responsible for the deviations.

The measured dimensions of both patch 1 and patch 2 corresponded well with the antenna

model.

Board 3, which is the top layer of the antenna, has a thickness of 0.127 mm. The layer was

chosen to be thin to minimize the effect on the antennas properties. During the design of the

antenna element the mechanical properties of the top layer were not considered. This

oversight turned out to be a crucial mistake. The thin top layer was not rigid and a large bulge

11

Industry standard file that are used in producing PCBs

33

was formed on the antenna when it was mounted. This increased the distance between the

patches and therefore decreased the level of coupling between the patches which in turn lead

to changes in the input impedance.

This error was detected early and tried to be solved by adding a foam layer on top to press the

bulge down. The idea was to use a material with a low dielectric constant, in order to not

affect the properties of the antenna. It was assumed that the foam layer was so rigid that the

bulge was removed. New measurements did not show any large improvements, and it was

concluded that the bulge did not cause the deviations.

To isolate the error source the input impedance of only board 1 was measured. Doing this

would determine if the error source was located in the upper parts or the lower parts of the

antenna. The measured and simulated input impedance of board 1 are shown in Figure 20 and

Figure 21.

34

Figure 20: The simulated reflection coefficient (S11) of board 1 plotted in a Smith chart (a) and in dB as a

function of frequency (b).

35

Figure 21: The measured reflection coefficient (S11) of board 1 plotted in a Smith chart (a) and in dB as a

function of frequency (b).

Comparing Figure 20 and Figure 21 it is seen that the simulated input impedance and

measured input impedance are quite similar. It was therefore concluded that the error source

most likely was located in one of the two upper boards. This significantly decreased the

number of possible error sources. The remaining error sources were either a different

dielectric constant of the foam substrate or a wrong distance between the patches.

36

Simulations with different dielectric constants were conducted but no results matched the

measured results. This alternative was therefore eliminated as a possible error source. Then

simulations with different distances between the patches were done and results similar to the

measured result were observed. One of these results is plotted in Figure 22.

Figure 22: Simulated reflection coefficient of the antenna element with a foam thickness of 3 mm plotted

in a Smith chart (a), and in dB as a function of frequency (b).

37

To obtain the results plotted in Figure 22 a distance between the patches of 3 mm was used.

This is an error of 0.7 mm. Comparing the simulated results in Figure 22 with the measured

results in Figure 17 similarities can clearly be seen. This was a strong indication that the

deviations were caused by the wrong distance between the patches. The assumption of a foam

layer rigid enough to remove the bulge was wrong and unnecessary time was spent in

searching for another error.

A new top layer was designed using the same type of substrate (Rogers RT/duroid 5880) with

a thickness of 1.575 mm. This thickness ensured that the substrate was rigid. The thick

substrate altered the input impedance of the antenna, and the dimensions of patch 2 were

therefore used to tune the input impedance in order to obtain a low reflection coefficient.

Simulated and measured results of this antenna are presented in chapter 5.

(a)

(b)

Figure 23: (a) A view of the three boards. (b) Side view of the modified antenna element.

38

3.4.2 Radiation pattern

Figure 18 and Figure 19 shows the simulated and measured radiation pattern of the antenna

element. Comparing the shape of these plots it is seen that good compliance between

measured and simulated results have been achieved, especially in the forward direction. The

simulated half-power beam width (HPBW) is 77° and the measured HPBW is 77.4°. Both

HPBWs is taken in the H-plane.

The large deviations between the antenna model and the manufactured antenna did not affect

the radiation pattern. The reason for this is, as discovered in [1], that the radiation properties

of the antenna is far less affected by changes in the geometry compared to the input

impedance. This means that deviations between the antenna model and the manufactured

antenna do not affect the radiation pattern as much as the input impedance.

39

4 Design of the array

In this chapter the design of the array antenna is presented. The design procedure is described

and all choices done during the design are explained. The original antenna element presented

in chapter 3 had to be modified owing to required element spacing and production cost. These

modifications are presented. Also methods for increasing the scan range are discussed, such as

DGS, EBG, and adaptive matching circuits.

4.1 Design procedure

A set of specifications are used as a starting point for a system design. For an array

specifications such as directivity, side lobe level, and scan range, are used to determine the

geometry and overall setup. For example a minimum requirement for the directivity gives a

limit on the minimum number of elements, and if a limit on the maximum side lobe level is

given, the use of a nonuniform amplitude distribution should be considered.

For this project the specifications are listed in Table 3.

Table 3: Specifications

Specification Value

Size 8x8

Frequency band 8 - 8.5 GHz

Polarization Linear

Scan direction Horizontal and

vertical

Maximum reflection coefficient -10 dB

Scan range Maximize

Grating lobes No

From Table 3 the first thing that can be noticed is that the size of the array is given. This puts a

limit on the maximum obtainable directivity of the array, as can be seen from equation (2.17).

No specification on maximum side lobe level was given and no limit was made. The reason

for this is that the side lobe level is reduced by individual amplitude weighting of the radar

channels and this is not part of the assignment. It should be mentioned that the use of an 8x8

array puts a limit on the minimum obtainable side lobe level for a uniform array. This can be

seen from Figure 2 in the theory chapter.

To determine the maximum element spacing without exciting any grating lobes a maximum

scan range needs to be set. Since it is specified that the scan range should be maximized one

could set the scan range to be to . No previous work was found where such a large

scan range was achieved. A scan range of to was therefore deemed as unrealistic.

40

Refs. [10], [11], [12] and [13] report that scan ranges close to to had been achieved.

The maximum scan range was therefore set to be to . This scan range applies in both

vertical and horizontal planes.

When developing the antenna element no mathematical model was found and therefore an

iterative trial and error process was used to design the antenna element. For an array

mathematical models do exist, as presented in the theory chapter. These were used to design

the array and predict its properties.

First the geometry of the array was determined. It was then discovered that the original

antenna element needed modifications, a new antenna element was therefore designed. A

model of the array was made in HFSS and simulated using the unit cell and Floquet port

simulation setup. This simulation setup was used to tune the input impedance of the array so

that a -10 dB reflection coefficient was achieved over as wide scan range as possible. To

increase the scan range several methods were investigated; electromagnetic bandgap materials

(EBG), defected ground structures (DGS) and adaptive matching circuits. Because of

problems explained later none of these methods were used.

Reaching the specified scan range was a challenge, but [10]- [13] suggest that a large

bandwidth gives a large scan range. The bandwidth of the antenna was therefore increased,

and larger scan ranges were achieved.

To verify the simulation results obtained by using the unit-cell and Floquet ports simulation

setup a more extensive simulation setup was used, namely the Finite Array DDM method.

4.2 Array design

4.2.1 Geometry of the array

The geometry of the array means its mechanical structure, like the number of elements, the

spacing between elements, or the lattice structure. The geometry has a large effect on the

array properties, especially the radiation pattern. This can be seen from equation (2.25), which

is the array factor for a rectangular array. The geometry of the array will also to a lesser

degree affect the element pattern. The reason is that the level of mutual coupling between

elements is dependent on the distance and relative placement of these elements.

Important properties of a radar antenna are the half-power beamwidth (HPBW), the maximum

side lobe levels, and the grating lobes. In a radar application a narrow main beam is important

to achieve a high angular resolution. Low side lobe levels are important to eliminate

reflections through the side lobes. Grating lobes are not wanted since large amounts of energy

will be transmitted and received in unwanted directions, which will lead to detection of targets

at different directions than the main beam. The properties discussed above are all controlled

by the geometry of the array.

41

As shown in the theory chapter the width of the main beam is controlled by the number of

elements in x and y-direction, and the element spacing. So to obtain a narrow main beam

either a large number of elements, large element spacing, or both could be used. A large

number of elements will also reduce the side lobe levels. If the element spacing is larger or

equal to half the wavelength grating lobes will occur for large scan angles. This puts a limit

on the element spacing. The element spacing should be as large as possible without any

grating lobes occurring, so that the directivity is maximized and the mutual coupling between

elements is minimized.

Since an 8x8 array was specified the only parameters left to decide for the geometry was the

lattice structure and element spacing and . A quadratic lattice structure was chosen, this

means that . This was done because the scan range in both x and y-directions should

be equal. It also gives the option for both horizontal and vertical polarization since the array

can be tilted 90° without any change in properties except for polarization.

To determine the element spacing equation (2.15) (repeated here for convenience) were used

to establish an upper limit on the element spacing.

(4.1)

This equation is derived for linear arrays, but will work for a quadratic array as shown in the

theory chapter. Using the wavelength corresponding to the highest frequency (8.5 GHz) and

. For an array scanned to the first grating lobe will occur at -90°, therefore

. This gives a maximum element spacing of 18.2 mm. Making the element

spacing smaller than 18.2 mm guarantees that no grating lobe will reach its maximum level

for the entire scan range. However, large parts of the first grating lobe will be visible if the

element spacing is not made small enough. HFSS was therefore used to find an element

spacing that reduced the grating lobe to the same level as the side lobes. This was achieved

with an element spacing of 16.5 mm.

4.2.2 Antenna element

Since the element spacing was determined to be 16.5 mm the antenna element needs to fit

inside a 16.5x16.5 mm2 area. The original antenna element could not fit inside this area and

therefore was made smaller. To achieve a smaller area the RF-transition was moved closer to

the via cage and the size of the via cage was reduced. These changes ensured that the antenna

element would fit inside the given area.

One of the specifications for the original antenna element was that electronic components

should be mounted directly on the backside of the antenna element. An extra layer of

substrate was therefore added. This specification was no longer valid and therefore the extra

component layer was removed. This reduces the production cost since one less substrate layer

42

is used. The SMA connector was placed directly over the RF-transition on the ground shield.

This removes the need for extra vias that connects the connector to a ground plane.

In chapter 3 the problems of using a too thin top layer were discussed. For the new design a

thicker substrate was therefore used. A thickness of 0.508 mm was chosen. This is still thin,

but together with a bonding material the problems encountered when using a thin top layer

should be solved.

The stack up of the new antenna element can be seen in Figure 24.

Figure 24: The new antenna stack up

From Figure 13 it is seen that the original antenna element had a hole in the ground plane

where the RF-transition ended. This was done to reduce the complexity of production, since

one less via type was needed. This hole in the ground plane was not optimal since it gave a

slightly skewed radiation pattern and increased levels of cross polarization. In the new

antenna element the hole was removed, as can be seen in Figure 24

To increase the bandwidth of the original antenna element the aperture coupled stacked patch

(ACSP) configuration as presented in the theory chapter was used. For reasons discussed in

more detail later in the report the ACSP configuration could not be used. Instead the resonant

aperture stacked patch (ASP) configuration was used. This means that the length of the slot

was increased to such an extent that the slot became a radiating element.

The final dimensions of the antenna element can be found in Appendix D

43

4.2.3 Element pattern

From pattern multiplication it is clear that the radiation pattern of an array is not only

dependent on the array factor but also on the single element pattern. It is therefore important

that the antenna element has a radiation pattern that fits the application. For this application

the optimal radiation pattern is shown in Figure 25(a)-(b). The two plots shows the radiation

pattern in the -plane and -plane. The optimal pattern in the -plane is a perfect half circle.

This means no radiation in the backwards direction, and a constant gain over

. Constant gain over the scan range is important since the main beam will not experience

scan loss. The optimal pattern in the -plane is a perfect circle (the antenna is

omnidirectional). This means that the main beam can be scanned in any -direction without

suffering scan loss. The optimal single element pattern shown here will enable a full scan in

the forward direction and remove all backwards radiation. The scan volume is a half -sphere.

This pattern is impossible to obtain in practice, but patch antennas can approximate it.

Figure 25: Optimal single element radiation pattern.

The radiation pattern of the antenna element is shown in Figure 26. Comparing this radiation

pattern to the optimal pattern in Figure 25(a) it is clearly seen that this radiation pattern is far

from optimal. It has a large backwards radiation and the gain decreases rapidly away from

broadside. This would lead to a large scan loss. This element pattern would severely degrade

the scanning performance of the array, making a scan range of to unwanted in a

practical application.

44

Figure 26: Normalized gain in dB for an antenna element, E-plane (φ=0°).

The pattern had to be improved and a search for possible solutions was conducted. It was

discovered that placing the antenna element in an array environment would improve its

radiation pattern. This can be seen in Figure 27, where the radiation pattern of an antenna

element placed in an infinite array is plotted. The reason for this improvement is the mutual

coupling between the elements. It is clear that this element radiation pattern is a better

approximation of the optimal radiation pattern. It has a more constant gain, at the gain

has only decreased by approximately 6 dB. The element radiation pattern is also more

symmetric, which is caused by the infinite array environment. This element radiation pattern

was a large upgrade and would give a much better scan performance.

45

Figure 27: Normalized gain in dB for an antenna element placed in an infinite array, E-plane ( ).

As mentioned this element radiation pattern is valid for elements placed in an infinite array.

Obviously an 8x8 array is not infinite. The infinite array assumption was expected to be a

good approximation for elements placed in the middle of the array. However, for elements on

the edges the radiation pattern will differ, due to diffraction on the edges and an uneven effect

from the mutual coupling. Simulations have been conducted to determine the edge element

radiation pattern and the results can be seen in chapter 5.

4.2.4 Increasing the scan range

A scan range of to for both the horizontal and vertical plane was the goal. Early in

the process it was realized that the goal was set very high. The reflection coefficient increased

rapidly for increasing scan angles, and scan ranges of only to was achieved in the

beginning. This of course was too low and additional methods to increase the scan range was

therefore investigated, such as; DGS, EBG, and adaptive matching networks. None of these

techniques ended up being used for reasons explained in later sections.

46

Wide scan ranges have been achieved in [10], [11], [12] and [13] using a similar antenna

element. None of these designs used any methods for reducing surface waves, nor were other

techniques presented that would increase the scan range. The only reason observed for the

large scan range was the large bandwidths. It was therefore suspected that a relationship

between a large bandwidth and a wide scan range existed. Because of this suspicion the

antenna element was redesigned to increase its bandwidth.

The original antenna element used an aperture coupled stacked patch configuration (ACSP) to

achieve a bandwidth of 13%. To increase the bandwidth of the antenna element the aperture

stacked patch (ASP) configuration was used. This meant that the length of the slot was

increased to a point where it became resonant. This would form an extra loop in the Smith

chart (see Figure 55(c) in Appendix A.1), and therefore increase the bandwidth. The length of

the slot was initially set to , where is the wavelength in the substrate. should be

the length where the slot becomes resonant. HFSS was then used to optimize the length.

Using the ASP configuration increased the bandwidth significantly and the scan range

increased immediately. One drawback using the ASP configuration is the increase in

backwards radiation since the slot now is a radiating element. Due to the ground shield and

the via cage no significant increase in backwards radiation was observed.

4.2.5 Tuning

As stated several times earlier the mutual coupling between elements will affect the input

impedance of the antenna elements. It was therefore necessary to re-tune the antenna element

to achieve an acceptable reflection coefficient. The input impedance is also dependent on the

scan angle, and this effect was accounted for when the array was tuned.

To tune the antenna element HFSS was used. Three methods for simulating arrays are

presented in chapter 2; the Finite array method, the Finite array DDM, and the unit-cell with

Floquet port. The last option was used during the tuning because of its low simulation times.

This method places the antenna element in an infinite array environment. It accounts for

mutual coupling and scan blindness, but not edge effects because of the infinite array

assumption. For larger arrays the infinite array assumption will give accurate simulation

results, especially for the input impedance and element pattern of the central elements. This is

confirmed by [9] which used the unit-cell method to design an 8x8 array, and good

compliance between simulated and measured results was achieved.

The antenna element was tuned using guidelines from [7]. The length of the patches was

adjusted to find the right resonance frequency and control the level of coupling between the

patches. The thickness of the antenna substrates was adjusted to find the right level of

coupling between the two patches and the slot. The level of coupling between the slot and the

lower patch, and the lower and upper patch should be balanced to achieve a large bandwidth.

The two different coupling levels determines the size of each loop in the Smith chart, if one

coupling level is much larger than the other it will dominate and one loop will be eliminated,

47

thus decreasing the bandwidth. The thickness of the antenna substrates are therefore very

important and the input impedance of the antenna is very sensitive for changes in the substrate

thicknesses.

Some problems achieving a balanced level of coupling was encountered. The reason for this

was later discovered to be the use of the H-shaped slot. This slot shape made the coupling

level between the slot and the first patch so big that it dominated the coupling between the

lower and upper patch. To achieve a balanced coupling level the thickness of antenna

substrate 1 was increased significantly. This lead to an increase in the mutual coupling

between elements since more surface wave modes was excited (see equation (2.52)). An easy

solution to this problem would be to use a rectangular slot. This would decrease the level of

coupling between the slot and the lower patch approximately by a factor of three and therefore

a thinner antenna substrate 1 could have been used. Unfortunately this was not considered at

this stage and the rectangular slot was therefore not used in this design.

The tuning was done in several iterations. When an acceptable scan range was achieved a

simulation using Finite array DDM simulation setup was conducted to verify the design.

4.2.6 Production

The array consists of 64 antenna elements placed in a quadratic lattice structure. Expanding

the antenna element into an array does not add significant complexity to the manufacturing

process since the antenna elements are patch antennas. Etching 64 identical geometries in a

periodic pattern on a substrate does not increase the complexity significantly.

The complete stack up of the antenna element can be seen in Figure 24. It is built up of five

substrate layers. It has two types of blind vias; ground shield to ground plane, and ground

shield to feed layer. Eliminating the buried vias used in the original antenna element

simplifies the manufacturing process. Only two curing cycles are needed to bond the three

lower layers.

The original antenna element was produced in three parts and plastic screws were used to

connect them. The reason for this was that no bonding material with low enough cure

temperature and pressure was found. The foam layer cannot handle high temperature and

pressure without being deformed. Using plastic screws to hold the array together is not a good

solution. The antenna input impedance is very sensitive to deviations in thickness of the

different layers. Using screws will most likely introduce an error in the distance between the

patches and therefore alter the input impedance.

It was decided to use two bonding materials to achieve a good bond between the three lower

layers and the foam layer could be attached without using high temperature. For the bottom

three substrate layers a bonding material from Taconic (FR-26-0025-60) should be used. This

material was used in the original antenna element and a good bond was achieved. Advantages

are the low loss tangent, a thin pressed thickness, and it can handle multiple bonding cycles.

For the two upper layers Tencate BF548 should be used. It has a low curing temperature of

48

82° and it works for foam structures. The properties of the two bonding materials are listed in

Table 4.

Table 4: Bonding materials

Type Dielectric constant Loss tangent Pressed thickness

FR-26-0025-60 2.60 0.0014 < 2.8 (mil)

Tencate BF548 3 0.017 -

The minimum size of the array was set when the element spacing was determined. An

element spacing of 16.5 mm gives a minimum array size of 132x132 mm2. To decrease the

effect of diffraction the array was made bigger, as can be seen in Figure 28. The array size

was chosen to be 400x400 mm2. This means that it is 134 mm from the edge element to the

edge of the antenna. This should reduce the diffraction and therefore reduce the backwards

radiation. The edge element radiation pattern should also be less affected.

Figure 28: Front view of the antenna array.

The full schematic of the antenna can be found in Appendix D

49

4.3 Mutual coupling

Since mutual coupling affects the arrays properties it was necessary to get a deeper

understanding of the mutual coupling in the array. Especially interesting was it to see how

large portion of the mutual coupling was due to surface waves, also the element spacing effect

on the mutual coupling levels was investigated.

A 2x2 quadratic array was modeled in HFSS using the same antenna elements as the main

array and the same element spacing. To determine the effect of surface waves on the mutual

coupling two versions of the array were simulated. One regular array, and one where the

antenna elements were separated by perfect electric conductor (PEC) walls. This effectively

stopped all waves traveling through the substrates. One could therefore compare the level of

coupling between elements with and without the waves traveling through the substrate. For

this antenna there are two types of waves traveling through the substrate; the surface waves,

and the parallel plate modes that is excited in the substrate between the two ground planes. It

was expected that the surface waves were the largest contributors since the via cage is shown

to effectively attenuate the parallel plate modes [1]. To confirm this a simulation was

conducted where PEC walls were used only for the two lower substrate layers. The results

showed no significant reduction in mutual coupling level compared to the array without PEC

walls. This meant that the parallel plate modes do not contribute much to the mutual coupling

level.

Simulations with different element spacing were also conducted. The results of the

simulations are presented in chapter 5.

4.4 DGS and EBG

Surface waves are a big problem when trying to increase the scan range, this have been

suggested by earlier work [9] and antenna literature [3, p. 866]. Therefore some work was

done to find methods which reduces surface waves. Two such methods were investigated and

are presented here. The first method is the use of electromagnetic bandgap materials (EBG),

and the second is use of defected ground structures (DGS).

4.4.1 EBG

Electromagnetic bandgap materials can be used in many applications. Of special interest here

is the use of EBG materials to attenuate surface waves. The EBG structure is a periodic

structure which works much like a band stop filter for surface waves [14]. By surrounding the

antenna element with EBG material the surface waves excited by the antenna element will be

severely attenuated. The EBG material is frequency dependent and should therefore be

designed for the center frequency of the antenna. EBG material consists of photonic crystals

which are made by cutting out defects in the substrate. It is a complicated process and difficult

to manufacture. For this reason the EBG was not an alternative for this design.

50

4.4.2 DGS

Defected ground structures is a method used to reduce surface waves. It works as a filter that

attenuates the surface waves at certain frequencies. DGS is a simple structure that consists of

an etched out shape (the defect) in the ground plane. This defect will alter the current

distribution on the ground plane and if the right shape and dimensions are used it will

attenuate the surface waves very effectively [15]. Several methods of reducing surface waves

are compared in [15], among them DGS and EBG. The presented results shows that DGS is

more effective in reducing surface waves than EBG. Due to the simple structure of the DGS

no additional steps to the manufacturing are needed. This makes DSG easier to realize and

will therefore save money. For these reasons DGS was chosen as the preferred option.

Figure 29: Three different ground defect structures. (a) Dumbbell (b) U-shape (c) back-to-back U-shape

In [16] three different shapes for the ground defect are compared; dumbbell, U-shape and

back-to-back U-shape. It is shown that back-to-back U-shape has twice the rejection

bandwidth as the other shapes. The reason for the increase in rejection bandwidth is that the

back-to-back U-shape is a cascade of U-shape defects. Cascading circuit elements leads to

broader rejection bands [16]. The back-to-back U-shape structure was therefore chosen since

it has the largest rejection bandwidth and therefore the best chance of covering the required

bandwidth of 8-8.5 GHz.

Figure 30: DGS test bench

51

A test bench was made with HFSS to tune the DGS. It consisted of two microstrip line stubs

placed between two layers of substrate, as can be seen in Figure 30. These stubs will excite

surface waves in the substrate. The distance between the two stubs was made large, so that the

coupling due to the surface waves was dominant. The test bench can be seen as a two port

network where S21 represents the coupling between the two stubs. The structure was tuned to

have a notch at 8.25 GHz. For comparison, an equal model was built only without the DGS.

The results are plotted in Figure 31.

Figure 31: S21 with DGS and without DGS.

Comparing the two plots it is clear that the DGS effectively reduces the coupling. The center

frequency is 8.19 GHz instead of 8.25 GHz. An attenuation of 24 dB is achieved at the center

frequency and the 3 dB rejection band covers the required frequency band of 8-8.5 GHz.

The tuned DGS was then used in the array. No improvement on the arrays scan range was

observed. It was suspected that the ground shield that is placed behind the first ground plane

to reduce backwards radiation affected the DGS. The test bench was modified with a second

ground plane and simulations showed that the ground shield removed the effect of the DGS.

Removing the ground shield was not an alternative since it is very important to minimize the

backwards radiation. The DGS was therefore abandoned.

52

4.5 Adaptive impedance matching

During the design of the array severe problems with increasing the scan range were

encountered. This led to an extensive search for techniques that could be used to increase the

scan range. One possible solution was found in [17]. Here an array of probe fed patch

antennas was loaded with varactor diodes to increase the scan range. Each patch is connected

to an varactor diode which is connected to ground. By changing the bias voltage over the

varactor diode the input impedance of the antenna is changed. This means that the antenna

can be matched for several different scan angles only by adjusting the bias voltage.

Connecting a varactor diode to every patch in the array would be highly impractical, because

of the added complexity to the manufacturing. For this reason the method was disregarded,

but it was a starting point for a possible solution to the scan range problem.

If the varactor diode is moved from the patch to the input terminal of the antenna element, and

a circuit being able to sense the reflected power and control the bias voltage over the varactor

is added one would have a system that could automatically match the antenna. Figure 32

shows a block diagram of such a system.

Figure 32: Block diagram of general adaptive impedance matching system

The matching network could be any topology that fits the matching requirements, the only

demand is that it consists of some type of variable circuit element. The sense block represents

a circuit that senses the reflected power and turns it into a signal the control unit can interpret.

This is often a voltage level. The control unit compares the output of the sense circuit with a

reference and decides what kind of control signal it should give the matching network. This is

a basic adaptive matching circuit.

If an adaptive matching circuit is to be used to increase the scan range of the array several

criteria has to be met. First it should be a space efficient and simple circuit since 64 circuits

53

has to be placed directly behind the array. The matching network should have a frequency

band broad enough to cover the required frequency band. This is important so that the system

only has to retune the matching for different scan angles. The control unit should be made

without using microcontrollers, FPGAs or memory, this requirement is given to keep the

complexity of the circuit down. Because of the large amount of power applied to each element

the sense circuit should ideally transmit all of the input power through to the antenna.

It already exist many adaptive matching circuits with varying complexity and performance

Three different systems are presented in [18], [19] and [20].

The sense circuit is often realized using a directional coupler as shown in Figure 33. The input

power is applied on port 1, most of the power goes to port 2 continuing on to the matching

network. Some power will be coupled to port 3. Port 4 is isolated. Some of the power will be

reflected at the input terminal of the matching network. The reflected power will hit port 2 of

the directional coupler and be coupled to port 4. Port 4 is connected to a circuit that converts

the reflected power to a signal the control unit can interpret.

Figure 33: Directional coupler.

The level of coupling should be low so that only a small portion of the input power is lost.

The low coupling level should not be a problem since a amplifier can be connected to port 4.

Some of the input power will be lost due the coupling between port 1 and 3, this could be seen

as a major drawback but [19] uses the coupled input power to its advantage. By comparing the

phase difference between the reflected power and the input power (the phase of the reflection

coefficient) the nature of the mismatch can be determined. For a positive phase difference the

mismatch is inductive and for a negative phase difference the mismatch is capacitive [19].

Knowing the type of mismatch is a large advantage and leads to a simpler control unit. If the

mismatch is inductive more capacitance is added to the matching network, and opposite if the

mismatch is capacitive.

The matching network can be realized using any type of matching topology. A pi network is

used in [20], a triple stub tuner is investigated in [18], and a simple LC circuit is used in [19].

These circuits uses variable capacitors to control the match. The variable capacitors can be

54

either varactors or switched capacitor arrays. Due to the large input power and high frequency

it is not certain that elements for this application can be found.

As stated earlier the control unit should be made without complex digital circuitry. This could

limit the performance of the adaptive matching circuit since the control algorithm has to be

relatively simple.

Developing an adaptive matching circuit was found to be too time consuming and complex

for this project. A simpler solution (increasing the bandwidth) was therefore chosen.

However, further work on this subject would be of interest since a good adaptive matching

circuit could improve the array performance. It will also make the array less affected by

production errors and inaccuracies in the simulator since the matching circuit would tune out

these error sources.

55

5 Results

This chapter presents results from the design. First simulation results and calculated results

for the array are presented. Then measured results of the modified antenna element are

presented.

5.1 Array

Since time did not allow for production of the array, only simulation results will be presented.

The simulation results obtained using HFSS will be compared to computed results obtained

using equations presented in the theory chapter.

5.1.1 Input impedance and scan range

Using the unit-cell Floquet port setup, the array input impedance has been simulated. Figure

34 shows the reflection coefficient for an antenna element placed in an infinite array

environment.

56

Figure 34: S11 plotted in (a) a Smith chart (b) in dB as a function of frequency. .

For an array the input impedance will change as a function of scan angle. Figure 35 plots the

reflection coefficient over a scan range of 0°-70°.

57

Figure 35: Reflection coefficient at different scan angels (a) E-plane scan ( ) (b) H-plane scan

( ).

58

To verify the accuracy of the unit-cell Floquet port simulation setup the array was simulated

using the Finite array DDM method. The reflection coefficient of a few different elements are

plotted in Figure 36

Figure 36: Reflection coefficient of different antenna elements for the array in broadside.

The notation (x, y) represents the placement of the element in the array. It is seen comparing

Figure 36 to Figure 34(b) that large deviations between the two simulation setups exist. Also

the reflection coefficient is above -10 dB in the entire frequency band, meaning that the

antenna is not matched.

Some important antenna properties are listed in Table 5

Table 5: Simulation results for array

Parameter Value Unit

-10 dB reflection coefficient

bandwidth at broadside 48 %

Scan range E-plane -55° to 55° deg

Scan range H-plane -45° to 45° deg

Radiation efficiency >0.96

59

5.1.2 Floquet analysis

Figure 37 shows the results of the Floquet analysis. Two different Floquet modes are plotted

together with the reflection coefficient for three different frequencies. These plots show how

much of the input power is transmitted to each Floquet mode. Mode 1 is the first propagating

Floquet mode and represents the major lobe and Mode 2 is the second propagating Floquet

mode and represents the first grating lobe.

Figure 37: Plot of Floquet modes for (a) 8 GHz, (b) 8.25 GHz, (c) 8.50 GHz.

60

5.1.3 Radiation

HFSS uses pattern multiplication to determine the radiation pattern of the array. As stated in

chapter 2 pattern multiplication does not include the effect of mutual coupling. However,

HFSS uses the element radiation pattern of an antenna element placed in an infinite array

environment, so the effect of mutual coupling on the element radiation pattern is included.

Figure 38 shows the normalized gain of the array scanned in four different directions.

Figure 38: Polar plot of the normalized antenna gain in dB at 8.25 GHz for (a) the array in broadside,

φ=0°, (b) the array scanned in , , (c) the array scanned in , , (d) the array

scanned in and , .

61

The element radiation pattern of an antenna element placed in an infinite array environment is

shown in Figure 39(a). To verify this result an 8x8 array is simulated using the Finite array

DDM method. The radiation pattern for a central element is plotted in Figure 39(b), and the

radiation pattern for an edge element is plotted in Figure 39(c).

Figure 39: (a) Normalized gain for an antenna element placed in an infinite array, φ=0°, (b) normalized

gain for a central antenna element, φ=0°, (c) normalized gain for an edge antenna element, φ=0°.

For more radiation patterns see Appendix C

62

Some important radiation properties are listed in Table 6

Table 6: Simulated radiation pattern properties

Scan angle Max Gain

(dB)

Directivity

(dB)

Side lobe

level (dB) HPBW

Real scan

angle

,

22.1 22.2 -13.6 14°

,

20.8 20.9 -11.5 15°

,

16.4 16.5 -8.7 31.4°

,

20.8 20.9 -24.3 16°

The side lobe level is calculated by comparing the largest side lobe level to the main beam. A

side lobe level of - 13.6 dB means that the largest side lobe is 13.6 dB below the main beam.

The real scan angle is the angle where the main beam has maximum gain.

To see the effect of the element pattern on the total radiation pattern, the array factor for all

four cases presented above are plotted in Figure 40. These plots are obtained using a Matlab

script provided by [3]. The Matlab script uses equation (2.25), which is the array factor for a

rectangular array

Radiation pattern properties of the array factor are listed in Table 7.

Table 7: Radiation properties for array factor

Scan angle Side lobe

level (dB)

Directivity

(dB) HPBW

Real scan

angle

,

-13 22 13.8°

,

-13 21.2 16°

,

-13.5 18.5 70.1°

,

-25 21.6 16.3°

63

Figure 40: Normalized array factor of the array for scan angles (a) broadside, (b) and (c), and , (d) and

In the theory chapter equations for calculating HPBW and directivity are presented. It is

interesting to compare simulated and calculated results. The HPBW is calculated using (2.21)

and (2.33) and the directivity is calculated using (2.17) and (2.20). The results obtained using

theory are listed in Table 8.

64

Table 8. Calculated results

Scan angle Directivity

(dB) HPBW

,

8.7 13.6°

,

8.1 15.7°

,

4.1 39.8°

,

- 15.7°

Comparing the results it is seen that the calculated directivity deviates from the simulated

results. The reason for this deviation is equation (2.17), which do not model the directivity in

broadside accurately. A large array is assumed used when deriving (2.17) and an 8x8 array is

probably not large enough for this assumption to be correct.

Equation (2.20) (repeated here for convenience) was derived to describe how beam

broadening affects the directivity.

(5.1)

To verify this equation a better value for than (2.17) provided was used, .

The simulated and calculated directivity are plotted in Figure 41.

Figure 41: Simulated directivity compared to calculated directivity

65

5.1.4 Mutual coupling

An investigation on mutual coupling in the array was conducted using HFSS and the results

are presented below.

Figure 42: Results from simulations of mutual coupling using element 1 as reference. (a) Standard array

(b) With PEC walls. An element distance of 16.5 mm is used.

Figure 42(a) shows the level of coupling between the elements of an 2x2 array, while Figure

42(b) shows the level of coupling in the same array, when the elements are separated by

walls of a perfect electric conductor (PEC). It is seen that the coupling level has been reduced

in Figure 42(b).

Figure 43 shows the level of mutual coupling between element 1 and 2, and element 1 and 3

for different element spacing.

66

Figure 43: Mutual coupling levels in a 2x2 array for different element spacing.

Measurements of the mutual coupling between two of the original antenna elements was

conducted with an element spacing of 50 mm. The results are plotted in Figure 44.

Figure 44: Mutual coupling between original antenna elements. (a) E-plane, (b) H-plane. Element spacing

of 50 mm.

There is no physical contact between the two elements so it is assumed that no surface waves

contribute to the mutual coupling.

67

5.2 The antenna element

Simulated and measured results of the modified antenna element as presented in chapter 3 are

presented in this section.

5.2.1 Simulation results

The most important results are listed in Table 9.

Table 9: Simulation results for the modified antenna element

Parameter Value Unit

-10 dB reflection coefficient bandwidth 16 %

-20 dB reflection coefficient frequency band 8-8.45 GHz

Realized center frequency 8.29 GHz

Maximum gain 8.4 dB

Radiation efficiency >0.96

Figure 45 shows S11 or the reflection coefficient plotted in a Smith chart and in dB as a

function of frequency.

68

Figure 45: S11 plotted in (a) a Smith chart (b) in dB as a function of frequency

Figure 46 and Figure 47 shows the normalized gain of the antenna at 8.25 GHz.

Figure 46: A polar plot of the normalized antenna gain in dB (8.25 GHz), H-plane (ϕ=90°).

69

Figure 47: A polar plot of the normalized antenna gain in dB (8.25 GHz), E-plane (ϕ=0°).

The HPBW of the antenna element is determined from Figure 46 and Figure 47. It is

approximately 78° in the H-plane, and in 58° in the E-plane.

70

5.2.2 Measured results

5.2.2.1 Input impedance

The input impedance of the antenna element was obtained using a network analyzer. The

result is plotted in Figure 48. A frequency band of 7.4-8.4 GHz with a center frequency of 7.9

GHz is achieved.

Figure 48: The measured reflection coefficient (S11) of the modified antenna element plotted in a Smith

chart (a) and in dB as a function of frequency (b).

71

The antenna reflection coefficient has been measured for varying the distance between the

two patches. The results are plotted in Figure 49 and Figure 50.

Figure 49: Reflection coefficient of the antenna element plotted in a Smith chart for different distances

between the patches. (a) 1.32 mm (b) 1.65 mm (c) 2.02 mm (d) 2.2 mm

72

Figure 50: Reflection coefficient of the antenna element plotted in dB as a function of frequency for

different distances between the patches. (a) 1.32 mm (b) 1.65 mm (c) 2.02 mm (d) 2.2 mm

Figure 49 shows that decreasing the distance between the patches makes the loop bigger,

owing to a larger coupling level between the patches. This leads to the center frequency being

moved up in frequency as seen in Figure 50.

73

5.2.2.2 Radiation pattern

Measurement of the antenna element radiation pattern was conducted at the antenna hall at

NTNU. Both E-plane and H-plane patterns were measured. Additional measurements were

conducted to determine the cross-polarization. The results are plotted in Figure 51 and Figure

52.

Figure 51: Radiation pattern for the modified antenna element at 8.25 GHz in normalized dB, (a) E-plane,

(b) H-plane

74

Figure 52: Cross polarization level of the modified antenna element

The measured HPBW is 55° and 84° in E-plane and H-plane, respectively. For more

measured results see Appendix B.

75

6 Discussion

6.1 Array performance

In this project emphasis was put on achieving a large scan range. A scan range of -55° to 55°

in the E-plane ( ) and -45° to 45° in the H-plane ( ) plane has been achieved.

The goal was a scan range of -70° to 70° in both planes. This goal was not reached within the

time limits for this thesis and more work is therefore needed. It is possible to achieve a scan

range close to the goal, this is confirmed by [10]- [13]. Here scan ranges close to -70° to 70°

have been achieved using similar antenna elements. Increasing the scan range is a difficult

task since the input impedance is highly dependent on the scan angle due to the mutual

coupling between elements.

Figure 35 shows the reflection coefficient plotted as a function of scan angle. It is seen that

the reflection coefficient is close to -10 dB over a large portion of the scan range in both

planes. A reflection coefficient of -10 dB is considered a match, but it will lead to large

amounts of power being reflected. For an input power of 50 W, 5 W will be reflected back

into the TX/RX circuits. This amount of reflected power can in worst case damage the system,

and it certainly makes the system less effective. The reflection coefficient should therefore be

decreased. If the reflection coefficient is decreased to -20 dB, only 0.5 watt will be reflected.

The scan range is greater in the E-plane than in the H-plane. This is a normal property for

these types of arrays, as seen in [10]- [13]. A reason for this is that the level of coupling

between elements differs from one plane to the other. This can be seen in Figure 42, which

shows that the coupling level in the E-plane is 3.6 dB larger than in the H-plane. This means

that the largest scan range is achieved in the plane which has the largest mutual coupling

level. This is an unexpected result since it was expected that the plane with the lowest mutual

coupling would have the largest scan range.

A correlation between large bandwidth and large scan range was suspected since [10], [11],

[12] and [13] achieved large scan ranges using only antenna elements with large bandwidths.

For this reason the was the bandwidth of the antenna element increased to 48% which is a

significant increase compared to the bandwidth of the original antenna element. After

increasing the bandwidth an increase in scan range was observed. This supported the

suspicion of a relationship between bandwidth and scan range. Further investigation into this

subject could be of interest to uncover if there truly is a relationship between bandwidth and

scan range, and if so, how strong the relationship is.

Figure 37 shows the results using the Floquet analysis. The two propagating modes are plotted

together with the reflection coefficient. The first mode represents the main beam, it is seen

that a large amount of the input power is transmitted in this mode. The second mode

represents the first grating lobe. It is observed that for larger scan angles more input power is

76

transferred to this mode. This is expected since grating lobes are more prominent at larger

scan angles. It is also observed that more power is transmitted in this mode as the frequency

increases. This can be understood by looking at equation (2.15). If the element spacing is kept

constant and the wavelength is decreased grating lobes will occur for lower scan angles.

For arrays of patch antennas a typical problem is scan blindness. Figure 35 and Figure 37

shows that no scan blindness will occur inside the scan range.

The unit-cell Floquet port simulation setup was used to tune the antenna. To verify the results

obtained with the simulation setup the Finite array DDM method was used. This method

should be more accurate since an actual 8x8 array is simulated. The results of the simulation

are shown in Figure 36. Large deviations between the two methods are observed. Some

deviations were expected because of the infinite array assumption, especially for the edge

elements. However, large deviations occur for both central and edge elements. Two possible

reasons for the deviations are considered likely. The first alternative is that an 8x8 array is not

large enough to be modeled accurately by an infinite array. The second alternative is the

possible wrong use of one of the simulation setups. If the first alternative is the reason it

means that the unit-cell Floquet port setup cannot be used to tune the antenna. This will make

the design process a lot more demanding since the Finite array DDM method needs

approximately three days to simulate the array. It is therefore not an effective method for

array tuning. Further investigation is needed to determine if the infinite array assumption is

the reason for the deviations.

A radiation efficiency of 0.96 was achieved. This is a good result, and was expected since the

antenna element designed in [1] had a similar radiation efficiency. The high radiation

efficiency is due to the low loss tangents in the materials used in the antenna. A high radiation

efficiency is important in this application since large amounts of power will be delivered to

the antenna. Assuming a 50 W input signal for each antenna element. The antenna will accept

45 W with a reflection coefficient of -10 dB. 43.2 W will then be radiated since the radiation

efficiency is 0.96. This means that 115.2 W will be dissipated as heat in the antenna. This is a

large amount of power gathered on a relatively small area (400x400 mm2), so methods for

transporting heat are important. This analysis has not taken into consideration the fact the

radar uses pulses. This means that the average power applied to the array will be lower.

In patch antennas the main limitation on scan range is surface waves [3, p. 866]. This has

been shown in [9] where decreasing the surface waves led to an increase in scan range. In [9]

electromagnetic band gap (EBG) material was used to decrease the surface waves. EBG

material was found to be too complex to manufacture and was therefore not used in this

design. Instead a defected ground structure (DGS) was tested. Good results were achieved in

the test bench. The DGS structure attenuated the surface waves by as much as 24 dB.

However, implementing it in the array did not increase the scan range. Further testing showed

that the ground shield severely reduced the DGS ability to suppress surface waves. It could

therefore not be used in this application.

The use of an adaptive matching circuit was investigated to improve the scan range and

reflection coefficient. It was concluded that an adaptive matching circuit would be too time

77

consuming and complex to develop. However, it is expected that it would have significantly

improved both the scan range and the reflection coefficient. Another advantage is that the

required accuracy on both the simulator and manufacturer would be less since the circuit will

tune out errors. A big disadvantage is the added complexity caused by the circuit and the extra

space it will use. However, use of an adaptive matching circuit could be necessary to reach

the scan range and reflection coefficient specifications.

To summarize, the scan range is too low in both planes and the reflection coefficient should

be lower to reduce the amount of reflected power. The main reason for the low scan range is

the strong mutual coupling between the elements in the array, caused mostly by surface

waves. To increase the scan range the bandwidth can be further extended, techniques to

reduce the surface waves can be used, or an adaptive matching circuit can be developed.

6.2 Radiation

The array has a half-power beamwidth (HPBW) of 14° when scanned in broadside direction.

For an uniform quadratic array the HPBW is mostly dependent on the number of elements and

the element spacing. Since an 8x8 array was specified in the project description a limit on the

minimum achievable HPBW was already set. The HPBW of the array factor was calculated

using equation (2.33). This resulted in a HPBW of 13.6°, which is a good prediction of the

simulation result. The small difference is probably caused by the effect the element pattern

has on the total radiation pattern.

When scanning the main beam away from broadside the HPBW increases, as seen in Figure

38. This is due to the beam broadening of the array factor and is modeled by (2.20), (2,21)

and (2.33). Beam broadening occurs since the effective length of the array decreases when the

scan angle increase. The HPBW is inversely dependent on the dimension of the radiating

element and it will therefore increase when the effective length is decreased. The simulated

HPBW increased from 14° to 31.4° when the array was scanned from broadside to 70°, giving

a large decrease in the angular resolution of the radar.

A beam broadening factor of was derived in the theory chapter. It can be applied on

both directivity and HPBW. The directivity decreases by a factor of and the HPBW

increases by a factor of when the main beam is scanned away from broadside. This

is a simple model which roughly estimates the beam broadening effect. Figure 41 shows the

calculated directivity and simulated directivity as a function of scan angle. It is seen that the

calculated directivity is very accurate up to about 10°, after that the differences are noticeable.

At 30° the difference is about 0.7 dB, which corresponds to an error of 17%. This is an

acceptable error for a simple model like this. It is concluded that the model can be used as an

estimate for scan angles near broadside.

A side lobe level of -13.6 dB is achieved when the array is scanned in broadside direction.

This side lobe level is high for radar applications [21, p. 544] and can lead to false detections.

The side lobe level is mostly dependent on the number of elements used, so to achieve a lower

78

side lobe level a larger array must be used. Another solution is the use of non-uniform

amplitude distributions such as a Binomial distribution or a Dolph-Tschebyscheff distribution

[3, p. 325].

It is observed that when scanning the array away from broadside the side lobe level increases.

This can be explained by using pattern multiplication. The side lobe level of the array factor is

relatively constant for different scan angles, as seen in Table 7, but the gain of the element

pattern is not constant over the entire scan range as seen in Figure 27 and Figure 39. The

element pattern has largest gain at broadside. The gain then decreases to the sides, and is

approximately 6 dB lower at 70°. When the main beam is scanned away from broadside it

will experience more scan loss, while the side lobes will experience less scan loss since they

now are located nearer broadside. This will the cause the side lobe level to increase.

Another problem experienced when scanning the array far away from broadside is that the

real scan angle will deviate from the wanted scan angle. This can be seen in Figure 38 where

the array is scanned to 70° but the real scan angle is only 63°. The reason for this is a

combination of beam broadening and scan loss. At 70° the array factor has a calculated

HPBW of 39.8°. This means that the difference in gain at 70 ° and 60° is small. So when the

array factor is combined with the element factor that has a higher scan loss at 70° than at 60°,

the maximum will be moved closer to 60°. How much it moves depends mostly on the

difference in gain between 60° and 70°.

As shown in Figure 40 the array factor is symmetric around the x-y-plane. This means that the

array factor radiates the same amount of power in the backwards direction as in the forward

direction. Therefore, to achieve a low backwards radiation it is important that the element

pattern cancel out as much of the radiation below the x-y-plane as possible. Low backwards

radiation is achieved, especially for the broadside scan where the largest level of backwards

radiation is -27 dB. For other scan angles the backwards radiation is always lower than -20

dB.

To increase the bandwidth the ASP configuration was used. This meant that the slot length

was increased until the slot became resonant. Since the slot became a radiating element an

increase in backwards radiation was expected. No such increase in backwards radiation was

observed. This means that the ground shield and via cage successfully reduced the backwards

radiation.

Figure 38(c) shows the gain pattern of the array scanned to 70°. It is observed that the grating

lobes is 30 dB below the maximum. The element spacing of 16.5 mm should have reduced

grating lobe level to the same level as the side lobes as seen in Figure 40(c). The much larger

reduction is due to the element pattern which has a high scan loss at 90°.

Figure 39(a) shows the element radiation pattern of an antenna element placed in an infinite

array environment. It has a smooth pattern with a maximum scan loss of 6 dB. Figure 39(b)

shows the element radiation pattern of a central element in an 8x8 array. It is not as smooth as

the first pattern, but has a relatively constant gain over the required scan range, with a

maximum scan loss of approximately 6 dB. It has a larger backwards radiation than the

79

infinite array element because of the diffraction on the edges of the array which is not

accounted for in the infinite array. Otherwise the infinite array element is a good

approximation. Figure 39(c) shows the element radiation property of an edge element. The

effect of the diffraction is clearly seen as the pattern is skewed. One method to reduce the

effect of the edge element pattern on the total radiation is to apply amplitude taper. This is a

method used to reduce side lobe levels but it will also decrease the effect of the edge element

pattern on the total radiation. This is done by applying less power to the edge elements than to

the central elements. The edge element pattern will be weaker and it will therefore affect the

total radiation pattern less [2, p. 106].

A scan range of -70° to 70° was the goal for the array. After studying the radiation properties

of the array it is clear that this goal is set to high. Even if a scan range of -70° to 70° is

achieved, the radiation properties at wide scan angles are too poor to be used in a radar

application. The main reasons for this is the large HPBW which leads to a very bad angular

resolution, and failure to achieve the wanted scan angles. These problems can be solved by

increasing the number of elements.

6.3 Mutual coupling

Figure 42(a) shows the mutual coupling levels in a 2x2 array. It is seen that the coupling

between element 1 and 3 is 3.6 dB larger than the coupling between element 1 and 2. The

reason for this is that surface waves will couple more strongly in the E-plane direction. Since

the fundamental surface wave mode is TM and the field for a rectangular patch in E-plane

direction is TM, they will couple more strongly [3, p. 858].

It was expected that the surface waves would account for a large portion of the mutual

coupling, and this is confirmed by Figure 42(b). It is seen that the coupling between element 1

and 3 is reduced by 4.1 dB and the coupling between element 1 and 2 is reduced by 2.7 dB

when perfect electric conductor (PEC) walls surrounds each element. This reduction is a clear

indication that surface waves are large contributors to the mutual coupling.

Figure 43 shows the coupling level as a function of element spacing. As expected the mutual

coupling is reduced when the element spacing increases. It was also expected that the

coupling level between element 1 and 3 should decrease more slowly than the coupling level

between element 1 and 2. The reason for this is that surface waves attenuates less than space

waves and the coupling level between element 1 and 3 is dominated by surface waves. This

expectation was not correct as seen from Figure 43. The coupling level between element 1

and 3 decreases rapidly until it reaches an element spacing of 30 mm, then it increases until it

flattens out at approximately -23 dB. A possible reason for this behavior is destructive

interference.

The mutual coupling level between two original antenna elements was measured, with the

results plotted in Figure 44. Since the two elements are separated by an air gap no surface

waves can travel between them. It is observed that the coupling level in both E-plane and H-

80

plane is almost identical. This confirms that the different coupling levels in the array is caused

by surface waves.

6.4 Antenna element

The original antenna element was designed during the specialization project last fall [1].

Chapter 3 summarizes the design and presents measured results of both input impedance and

radiation pattern. Large deviations between the measured and simulated results were

experienced. The main error source was found and the antenna element was redesigned.

Measured and simulated results of this modified antenna element was presented in chapter 5

and will be discussed here.

Comparing Figure 45(a) and Figure 48(a) it is seen that better compliance between measured

and simulated results has been achieved. The largest difference is the absence of the loop in

the measured results. This indicates that the level of coupling in the antenna is wrong. One

reason for this could be that the distance between the patches is high causing a too low

coupling level for the loop to be formed. The other reason could be that the distance between

the feed line and lower patch is low giving a too strong coupling level, and therefore

removing the loop. Thus the error source is probably either the thickness of antenna substrate

1 or 2. The accuracy of the simulator can also be a reason for the deviations.

The consequence of the lacking loop is a that the center frequency is moved approximately

350 MHz down in frequency. This can be seen in Figure 48(b). It is also observed that the -20

dB reflection coefficient frequency band is 7.67-8.13 GHz. So the antenna works very well

only at the wrong frequency.

Figure 49 and Figure 50 shows the effect of different thicknesses of antenna substrate 2 on the

input impedance of the antenna. It is seen that for smaller distances the loop is formed and its

radius increases. The center frequency is moved up in frequency, but the reflection coefficient

increases. These results confirm that the reason for the absence of the loop is wrong coupling

levels in the antenna due to errors in layer thickness.

A measured HPBW of 55° and 84° is achieved in E-plane and H-plane respectively. Which is

in good compliance with the simulated results (58° and 78°). Showing that HFSS can produce

accurate results. Studying Figure 51(a) carefully it is seen that the pattern is skewed. The

maximum gain occurs at approximately at 8°. The reason for this is the hole in the ground

plane where the RF-transition is located.

Figure 52 shows that the cross polarization level is approximately -30 dB. This means that the

antenna element has a high quality linear polarization.

81

6.5 Error sources

A significant error source is production errors. This has already been experienced as described

in chapter 3. The complicated structure of the antenna makes it difficult to manufacture and

therefore production errors are likely. Because of the high frequency small errors in the

dimensions can lead to large deviations in antenna properties. Measurements have shown that

the copper structures, such as the patches and transmission lines, are produced with good

accuracy, and are therefore not expected to cause large errors. The thickness of the different

substrates and bonding layers, however, are difficult to predict accurately. This leads to

differences between the manufactured antenna and the antenna model, and therefore

deviations between measured and simulated results. The thickness of the different substrates

are important parameters since they control the coupling between the slot and the patches.

Thus small errors in thickness will lead to a different input impedance. The large deviations

between measured and simulated results caused by production errors are a serious problem,

which makes it difficult to tune the antenna using HFSS.

Production errors will typically move the center frequency of the antenna, either up or down

in frequency. A possible solution is therefore to increase the bandwidth of the antenna. This

should make the antenna more robust against production errors since an acceptable reflection

coefficient would be achieved even if the center frequency is moved. Another solution is an

adaptive matching circuit. This will significantly relax the matching requirements since a

circuit automatically will match the antenna. The circuit will therefore adjust for production

errors.

Another error source is the infinite array assumption used when the array was tuned. It was

expected that an 8x8 array could be modeled as an infinite array with only small losses in

accuracy. The simulations however, indicated that this might not be the case.

6.6 Future work

The ultimate goal is to produce and perform measurements on the produced array. However,

first the array needs to be completely finalized. The scan range of the antenna needs to be

improved, and it is important that the reflection coefficient is decreased over the entire scan

range. A -20 dB reflection coefficient should be the goal. This will reduce the power reflected

back at the power amplifier to an acceptable level.

Before the array can be produced the deviations between the measured and simulated results

of the antenna element have to be reduced. This is important to achieve expected properties of

the produced array.

A large amount of power is planned to be applied to the array. Some of this power will be

dissipated as heat and therefore an increase in the antennas temperature is expected. It is

important to determine how high the temperature increases will be and what effects it will

have on the antenna. A rise in temperature will expand the antenna materials. This will lead to

82

deviations in the thickness of the layers, which again leads to deviations in the input

impedance. It could be necessary to tune the antenna at the expected work temperature.

Another consequence of high input power is the possibility of electric breakdown inside the

antenna. Because of short distances between the conductor and ground it is a possibility that

the large electric fields can lead to electric breakdown. This means that current will travel

from the conductor to the ground plane through the substrate. This is a detrimental effect that

has to be investigated further.

A short section on adaptive matching can be found in chapter four. This is an interesting topic

that deserves further work. An adaptive matching circuit would increase the scan range, lower

the reflection coefficient of the array, and make the design more robust against production

errors.

One of the reasons that low backwards radiation is important is the effect it can have on the

electronic components placed behind the array. The backwards radiation is lower than -20 dB.

More work is needed to ensure that this is low enough for the electronic components to avoid

damage.

83

7 Conclusion

An 8x8 array antenna has been designed using resonant aperture stacked patch (APS)

antennas as elements. It covers the required frequency band of 8-8.5 GHz, a linear

polarization is achieved and the backwards radiation level is below -20 dB.

HFSS was used to design and simulate the array. Both classical array theory and Floquet

analysis was used in the analysis of the array. Even though the two methods have completely

different approaches identical expressions for the maximum element spacing was derived.

A scan range of -55° to 55° in the E-plane and -45° to 45° in the H-plane was achieved. The

goal of a scan range of -70° to 70° in both planes was therefore not met. The main reason for

this is the large mutual coupling in the array mostly owing to surface waves. Methods to

increase the scan range, such as electromagnetic bandgap (EBG) materials, defected ground

structures (DGS), and adaptive matching circuits were investigated. Both EBG materials and

DGS increase the scan range by suppressing surface waves. EBG was too complicated to

manufacture and was discarded. DGS showed promising test results, but failed to suppress the

surface waves when implemented in the array. This was due to the ground shield. The

development of an adaptive matching circuit was deemed too time consuming and

complicated for this project. However, an adaptive matching circuit will significantly improve

the array performance. If the circuit is made simple and small enough it is a possible solution

to achieve a reflection coefficient lower than -20 dB over the entire scan range.

A reflection coefficient just below -10 dB have been achieved over the scan range. This result

should be lower considering that the power amplifier can deliver 50 W to the input terminal of

the antenna element. Almost 5 W will then be reflected back into the circuit. This could

possibly damage the system. A reflection coefficient of -20 dB or lower over the entire scan

range will lead to only 0.5 W being reflected back.

The array has a half power beam width (HPBW) of 14° at broadside. The HPBW increases as

the main beam is scanned away from broadside. This is a fundamental effect called beam

broadening and can be explained by the fact that the effective length of the array seen from

the observation point decreases when the main beam is scanned away from broadside. The

HPBW at a scan angle of 70° is 31.4°. This severely reduces the angular resolution of the

array. Other unwanted effects occurring when scanning the main beam are an increase in side

lobe level and wrong realized scan angles. The side lobe level increases from -13.6 dB at

broadside to -8.7 dB at a scan angle of 70°. Considering these effects it can be concluded that

a scan range of -70° to 70° is too large for this array due to the poor radiation performance at

large scan angles. One solution for reducing these effects is to increase the number of

elements. Individual weighting of the antenna channels will also reduce the side lobe level.

A radiation efficiency of 0.96 is achieved. This is a good result and is caused by the low loss

tangent in the substrates being used. A high radiation efficiency is important due to the large

84

amount of power delivered to the antenna. Assuming a reflection coefficient of -10 dB and 50

W being delivered to each antenna element, 115.2 W will then be dissipated as heat. This will

lead to a high antenna temperature. More work need to be done to determine the antenna

behavior at high temperatures.

Most of the simulation results presented in this report were obtained using an unit-cell Floquet

port simulation setup in HFSS. The unit-cell Floquet port simulation setup produces results

for an infinite array. It was expected that an 8x8 array is a close enough approximation of an

infinite array. Simulations done at the end of the project indicated that this assumption does

not hold and that results obtained using the unit-cell Floquet port simulation setup can be

wrong. Further investigation is necessary before a conclusion can be made.

An antenna element was produced and measured. Deviations between measured and

simulated input impedance were found. The reason is inaccuracies in the simulations and

production errors. The measured frequency band is 7.4-8.4 GHz where the center frequency is

at 7.9 GHz. This means that the center frequency is moved approximately 350 MHz down in

frequency. These deviations causes severe problems and the array cannot be produced until

the deviations are made smaller.

Good compliance between simulated and measured results of the radiation pattern was

achieved. The measured HPBW of the antenna element is 55° and 84° in the E-plane and H-

plane respectively, which is very similar to the simulated result.

To summarize, the array is still not ready for production. First the scan range and reflection

coefficient need to be improved. Then the deviations in simulated and measured results need

to be reduced, and topics such as the thermal properties of the array need to be investigated.

85

8 Bibliography

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radar antenna," Trondheim, 2012.

[2] A. K. Bhattacharyya, Phased Array Antennas, Wiley, 2006.

[3] C. A. Balanis, Antenna Theory, third edition, Wiley, 2005.

[4] D. K. Cheng, Field and Wave Electromagnetics, second edition, Addison Wesley, 1989.

[5] D. M. Pozar, Microwave Engineering, fourth edition, Wiley, 2012.

[6] R. B. Waterhouse, "Stacked Patches Using High and Low Dielectric Constant Material

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1767-1771, December 1999.

[7] R. B. Waterhouse, D. M. Pozar and S. D. Targonski, "Design of Wide-Band Aperture-

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vol. 46, no. 9, pp. 1245-1251, 1998.

[8] D. M. Pozar, "A Review of Aperture Coupled Microstrip Antennas: History, Operation,

Development and Applications," 1996.

[9] C. Fulton and W. Chapell, "Low-Cost, Panelized Digital Array Radar Antennas," in

COMCAS. IEEE, 2008.

[10] L. Infante, S. Mosca and M. Teglia, "Low-Profile Wide-Band Wide-Angle-Scan Antenna

Array Element," in 6th European Conference on Antennas and Propagation, 2011.

[11] R. Erickson, R. Gunnarsson, T. Martin, L. G. Huss, L. Petterson, P. Andersson and

Ouacha, "Wideband and Wide Scan Phased Array Microstrip Patch Antennas for Small

Platforms".

[12] L. G. Huss, R. Gunnarsson, P. Anderson and R. Erickson, "A Wideband, Wide Angle

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Profile Wide-Scan Phased Array for UWB Applications".

[14] Fu, Y. Yunqi and Naichang, "Elimination of Scan Blindness in Phased Array of

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Wireless Propagation Letters , vol. 3, pp. 63-65, 2004.

86

[15] M. Salehi and A. Tavakoli, "A novel low mutual coupling microstrip antenna array

design using defected ground structure," International Journal of Electronics and

Communications, pp. 718-723, 2006.

[16] S. Xiao, M. C. Tang, Y. Y. Bai, S. Gao and B. Wang, "Mutual coupling suppression in

microstrip array using defected ground structure," IET Microwaves, Antennas &

Propagation, vol. 5, no. 12, pp. 1488-1494, 2012.

[17] R. B. Waterhouse, "A Novel Technique for Increasing the Scanning Range of Infinite

Arrays of Microstrip Patches," IEEE Microwave and Guided Wave Letters, vol. 3, no. 12,

pp. 450-452, 1993.

[18] Smith, C. Natanael J, V. Chi-Chih and J. L, "An Improved Topology for Adaptive Agile

Impedance Tuners," IEEE Antennas and Wireless Propagation Letters, vol. 12, pp. 92-

95, 2013.

[19] Meng, v. B. Fanfan, M. Andre and Reza, "A Mismatch Detector for Adaptive Antenna

Impedance Matching," in Proceedings of the 36th European Microwave Conference,

Manchester, 2006.

[20] Ida, T. Ichirou, T. Jun-ichi and O. Y. Takeshi, "An Adaptive Impedance Matching

System and its Application to Mobile Antennas," IEEE, 2004.

[21] M. I. Skolnik, Introduction to Radar Systems third edition, McGraw-Hill, 2001.

[22] V. Rathi, G. Kumar and K. P. Ray, "Improved Coupling for Aperture Coupled Microstrip

Antennas," IEEE Transactions on Antennas and Propagation, vol. 44, no. 8, pp. 1196-

1198, 1996.

[23] D. M. Pozar and S. D. Targonski, "Improved Coupling for Aperture Coupled Microstrip

Antennas," Electronics Letters, vol. 27, no. 13, pp. 1129-1131, 1991.

[24] I. J. Bahl and K. C. Gupta, "Average power-handling capability of microstrip lines,"

Microwave, Optics and Acoustics, vol. 3, no. 1, pp. 1-4, 1979.

A-1

Appendix A: Additional theory

A.1 Patch antennas

A general patch antenna is shown in Figure 53. It consists of a layer of dielectric substrate

where a copper patch is etched on the top, and a ground plane is etched at the bottom. The

patch is the radiating element and can have any shape. The size of the patch, thickness and

dielectric constant of the substrate and feed type are parameters that determine the properties

of the antenna.

Figure 53: Patch antenna

Feeding methods

[3, pp. 813-815]

There are several different ways to feed a patch antenna; microstrip line feed, probe feed,

proximity feed and aperture coupled feed. A short presentation of each is given below.

A-2

Figure 54: (a) Microstrip line feed (b) Probe feed (c) Aperture-coupled feed (d) Proximity feed

Microstrip line feed: The microstrip line feed is shown in Figure 54 (a). The patch is fed by a

microstrip line connected to one of its sides. Matching is done by moving the contact point in

to the patch. It is easy to model and easy to produce. The feed line will radiate and disturb the

radiation pattern of the patch, this is called spurious feed radiation. Because of asymmetric

structure, high levels of cross polarizing will occur. The bandwidth is rather limited, typically

2-5%.

Probe feed: The probe feed is shown in Figure 54 (b). The inner conductor of a coaxial cable

is brought up through a hole in the ground plane and is connected to the patch, the outer

connector is connected to the ground plane. Good matching is achieved by moving the point

of contact to a place that gives the wanted input impedance. Since most of the feed is behind

the ground plane and the probe is behind the patch, the spurious feed radiation is significantly

reduced compared to the microstrip line feed. The probe feed suffers from low bandwidth and

the asymmetric structure that will lead to cross polarization.

Aperture-coupled feed: The aperture-coupled feed is shown in Figure 54 (c). The patch and

feed line are separated by a ground plane, so there is no physical contact between the feed line

and the patch. The fields are coupled from the feed line through a slot in the ground plane to

the patch. Since the feed is placed behind the ground plane the spurious feed radiation is low.

A-3

The structure is symmetric, this leads to low cross polarization. It is more complex to produce

than microstrip line feed and probe feed, but it has more parameters to tune the radiation

characteristics and input impedance. It has a low bandwidth, but several well documented

techniques have been developed that increases the bandwidth [7].

Proximity feed: The proximity feed is shown in Figure 54 (d). Similar to aperture-coupled

feed the proximity feed has no physical contact between the feed line and the patch. Here, the

feed line is placed directly under the patch, so the fields couples straight from the feed to the

patch. This configuration has the largest bandwidth of the alternatives presented here. The

spurious feed radiation will affect the forward radiation pattern more than the aperture-

coupled feed because no ground plane separates the feed from the radiating element. It is a

symmetric structure giving low cross polarization.

The feed method is chosen depending on the application. The proximity feed has the largest

bandwidth, so for applications where high bandwidth is needed, and no additional bandwidth

increasing techniques is used, the proximity feed is the best option. For large arrays the probe

feed and the aperture-coupled patch has an advantage since both enables feeding from the

back. This will simplify array design and phase-steering of the array. Microstrip line feed is

easy to match and the design is less complicated than the other options. This subject is further

discussed in the design chapter.

Techniques to increase bandwidth

Patch antennas have a rather low bandwidth so in this section three techniques for increasing

the bandwidth of an aperture-coupled patch antenna are presented.

Single patch resonant aperture: This configuration is a standard aperture-coupled patch

antenna as shown in Figure 54 (c). The size of the slot is increased to the point where it

becomes resonant, this means that the slot becomes a radiating element. The resonance of the

slot is coupled to the resonance of the patch, this is called mutual resonance. This will result

in a wider bandwidth as seen in Figure 55 (a). Here the reflection coefficient of the antenna is

plotted over different frequencies in a Smith chart. The tight loop around the center is the

result of the mutual resonance of the slot and patch. This configuration has been shown to

obtain a 1.5:1 voltage standing wave ratio (VSWR) bandwidth of over 20% [7]. A 1.5:1

VSWR is equivalent to a -14 dB reflection coefficient. The resonant aperture is an effective

radiating element and will increase the backwards radiation of the antenna.

Aperture coupled stacked patch (ACSP): In this configuration the slot is sized so that it is

not resonant, instead a second patch is placed at a height directly over the first patch, this can

be seen in Figure 56. The resonance of the lower patch couples to the resonance of the upper

patch. This will lead to the same result as the first alternative as shown in Figure 55 (b). The

tight loop in the Smith chart is formed because of the mutual resonances between the lower

and upper patch. The 1.5:1 VSWR bandwidth of this antenna can also be over 20% [7].

Resonant aperture stacked patch (ASP): This configuration combines the two methods

above to give the antenna a 1.5:1 VSWR bandwidth that can exceed 40% [7]. The resonance

A-4

of the slot is coupled to the resonance of the lower patch, then the resonances of the lower and

upper patch are also coupled together, resulting in two tight loops in the Smith chart, see

Figure 55 (c). As for the first alternative the ASP have a large backwards radiation due to the

resonant aperture.

Figure 55: Reflection coefficient plotted in a Smith chart for (a) Resonant aperture (b) The ACSP (c) the

ASP

To achieve a high bandwidth the reflection coefficient of the antenna, as plotted in Figure 55,

needs to be as close as possible to the center of the Smith chart over as many frequencies as

possible. Because of the tight loops formed as a consequence of the mutual resonances, the

reflection coefficient is closer to the center of the Smith chart over a lager range of

frequencies, and thus increases the bandwidth.

Aperture-coupled stacked patch (ACSP)

This antenna uses the aperture-coupled feed configuration as the feed mechanism and stacked

patches to increase the bandwidth. The ACSP is a complicated structure and no mathematical

model that can be used in the design has been found. However, some guidelines have been

developed [7] [8]. A brief summary of these guidelines and other aspects of the ACSP are

presented in this section.

Figure 56 shows the ACSP antenna. It consists of a feed substrate with a microstrip line

etched on the bottom and ground plane on the top. A rectangular slot in the ground plane is

placed directly over the feed line. The stub, which is the part of the feed line that is under the

slot, is used to match the antenna [7]. Two antenna substrates are placed on top of each other

over the feed substrate, with a rectangular patch etched on top of each substrate.

A-5

Figure 56: The Aperture Coupled Stacked Patch (ACSP)

When a signal is put on the feed the fields will couple from the feed line through the slot and

to the first patch. This is a strong coupling and is the reason for the large loop in the Smith

chart in Figure 57. Then a weaker coupling between the two patches resonances occur. This

results in the small loop in the Smith chart in Figure 57.

This antenna has been shown to have a 1.5:1 VSWR bandwidth of over 20 % [7] and achieve

a gain of 8-9 dB over a frequency band of 3.1-3.5 GHz [9].

One advantage of the ACSP is that multiple parameters can be used to tune the antenna. It

makes the design complicated but it allows for good control over the input impedance and

radiation characteristics. A description of these parameters and effects are found in [7]- [9]

and are summarized below.

A-6

Figure 57: Reflection coefficient of the ACSP plotted in a Smith chart

Patch length

The patch length controls the resonance frequency of the patch. For stacked antennas the

length also controls the level of coupling between patches and will therefore affect the

diameter of the little loop (D2) .

Patch width

The patch width affects the resonant resistance of the antenna, where a wider patch gives

lower resistance.

Slot length

The slot length controls the level of coupling between the feed and the lower patch. A longer

slot means higher coupling, which increases the radius of the large loop (D1). If made too big

relative to the wavelength the slot becomes resonant and will radiate. This can be used to

increase the bandwidth, as in the ASP antenna, but it will degrade the front-to-back ratio, due

to backward radiation.

Slot width

The sloth width affects the coupling level in a lesser extent than the slot length, and is

therefore held at 1/10 of the slot length.

Feed line width

The width determines the characteristic impedance of the feed line. Additionally, it controls to

a certain degree the coupling between the feed and patch. Thinner feed gives stronger

coupling.

A-7

Stub length

The stub length, which is the length of the stub taken from the center of the slot and out

controls the reactance of the slot. Thus it is an effective parameter to tune when matching the

antenna. A longer stub moves the impedance locus in the inductive direction in the Smith

chart and a shorter stub in the capacitive direction. It is usually around , where is the

wavelength in the substrate and is given as [5, p. 20]

(A.1)

where is the free space wavelength, and is the magnetic permeability and electric

permittivity respectively, and is the angular frequency. The last step can be made since

[4, p. 355].

Stub width

The stub width is used to match the impedance of the antenna since the width of the stub

controls the coupling level. A wider stub decreases the coupling level.

Feed substrate thickness

The thickness of the substrate will together with the feed line width and the dielectric constant

determine the characteristic impedance of the feed line. Thicker substrate gives a wider feed

line. Thin feed substrate gives less spurious feed radiation but greater loss.

Feed substrate dielectric constant

The dielectric constant is chosen so that the wanted feed line characteristics are obtained.

Antenna substrate thickness

The thickness is primarily used to control the coupling level between the different elements in

the antenna. The thicker the substrate, the more loosely coupled will the elements be. The

thickness of antenna substrate 1 from Figure 56 affects D1 and the thickness of antenna

substrate 2 affects D2. A thicker substrate will increase the bandwidth but also increase

surface wave loss.

Antenna substrate dielectric constant

The dielectric constant affects bandwidth and efficiency. A low dielectric constant gives less

surface waves and increases the bandwidth.

Slot

For an aperture coupled patch antenna the size and shape of the slot have a large effect on the

antenna properties. As mentioned earlier, the size of the slot controls the level of coupling and

it can also be used to increase the bandwidth if the slot is made resonant [7]. The shape of the

A-8

slot will also affect the coupling, since different shapes have different levels of coupling for a

given area.

When matching an aperture coupled patch antenna it is normal to adjust the size of the slot. If

the slot length approaches during the matching process, the slot becomes resonant. The

slot is then a radiating element and this will increase the backward radiation of the antenna.

This may be unwanted in many applications. Several different shapes have therefore been

investigated to find more effective apertures with regard to larger coupling than the

rectangular slot. Two such works are [22] and [23]. In [22] three different shapes; bowtie, H-

shape and hourglass are compared to the rectangular slot. All have superior levels of coupling

compared to the rectangular slot.

Figure 58: (a) Rectangular slot. (b) Bowtie slot. (C) H-shape slot. (d) Hourglass slot. (e) Dogbone slot

In [23] the dogbone slot, as shown in Figure 58(e), is presented. It is concluded that the

dogbone achieves over three times the level of coupling compared to a rectangular slot of the

same size. Since the H-shape and dogbone are very similar, it is reasonable to assume they

achieve approximately the same level of coupling.

The fields of the rectangular slot decrease rapidly when moving away from the center and

have to be zero at the ends. The fields for the other slots is also zero at the ends but because of

the different shapes a less rapid decrease in field strength occurs when moving away from the

center [23]. This leads to a more uniform field and an increased level of coupling.

A-9

Hi-Lo dielectric constant configuration

When designing a stacked patch antenna, different combinations of materials can be used to

give the antenna different properties. One such combination is the Hi-Lo dielectric constant

configuration presented in [6]. Here, the lower patch is etched on a substrate with a high

dielectric constant and the upper patch is etched on a substrate with lower dielectric constant.

The Hi-Lo configuration is shown to increase the bandwidth and surface wave efficiency, it

also reduces cross polarization [6]. Since a thick substrate, specifically the upper layer,

increases the bandwidth it is necessary that the upper layer have a low dielectric constant to

minimize surface waves.

A-10

A.2 Antenna parameters

This section presents a brief description of important antenna parameters used in the project.

First the input impedance and bandwidth are described, then the antenna efficiency and at last

the definition of antenna gain is presented.

Input impedance

[3, pp. 80-85]

The input impedance of an antenna is the impedance seen looking into the input terminals of

the antenna. It is computed as the ratio of the voltage to the current at the input terminal. From

Figure 59, which shows an equivalent circuit of the antenna. the impedance can be written as

(A.2)

where

(A.3)

models the loss in the antenna and is the radiation resistance of the antenna.

indicates how much power is radiated.

Figure 59: Equivalent circuit of an antenna

is the generator connected to the terminals, and and represents the internal

impedance of the generator, where is the resistance and is the reactance. For a patch

antenna and are dependent on the geometry, i.e. shape and size of the patch, and the

A-11

electrical properties of the material. The input impedance is dependent on frequency, and

models the dependency. An antenna is resonant when .

Bandwidth

[3, p. 70]

The bandwidth of an antenna is the frequency range where one specified antenna property is

achieved. A common bandwidth specification, specifically for patch antennas, is the -10 dB

reflection coefficient bandwidth. It gives the width of the frequency band where the reflection

coefficient is lower than -10 dB. Other parameters can be used to specify the bandwidth, for

example gain, radiation pattern and radiation efficiency. If not anything else is specified the -

10 dB reflection coefficient bandwidth is implied in this report.

The bandwidth can be given as a ratio of the lowest and the highest frequency, or as a

percentage of the center frequency. The latter is used in this report.

Antenna efficiency

[3, pp. 64-65]

The total antenna efficiency can be divided into three efficiencies; conduction efficiency

, dielectric efficiency and reflection efficiency . can be written as a function of the

reflection coefficient . The total efficiency is then given by

(A.4)

Since conduction and dielectric efficiency are hard to compute and measure separately they

are often combined into one efficiency . This efficiency describes the internal losses in the

antenna and is the same as the radiation efficiency which is defined as

(A.5)

where is the radiated power and is the accepted power. The radiation efficiency

describes how effective an antenna is at turning the accepted power into radiated power. A

low radiation efficiency means that a lot of the power accepted is lost in the antenna and is

dissipated as heat.

A-12

Gain

[3, pp. 65-68]

The gain is a very useful antenna parameter. It takes into account both the radiation efficiency

and the directivity. High gain means that the antenna is efficient and that the antenna directs a

lot of power in that direction. Gain is defined as [3, p. 66]

(A.6)

where is the radiation intensity and is the accepted power. The radiation

intensity in a given direction is given as [3, p. 40]

(A.7)

where is the radiation density and can be found from the time average Poynting vector.

Combining (A.5) and (A.6) gives

(A.8)

where is the directivity of the antenna and is defined as [3, p. 44]

(A.9)

is the radiation intensity of an isotropic source. The directivity gives a description of how

much power an antenna directs in a certain direction. If an antenna directs a large portion of

its radiated power in a certain direction it will have a large directivity in that direction.

Beamwidth

[3, pp. 42-43]

A parameter often used to describe the radiation pattern of an antenna is the beamwidth. It is

the angular separation between two identical points on each side of a maximum. There are

several standard beamwidth definitions but in this report only one definition is used, and that

is the half-power beamwidth (HPBW). The HPBW is defined as the angular separation

between two points on each side of a maximum where the points have half the radiation

intensity as the maximum.

A-13

The beamwidth is an important parameter when designing a radar antenna. The reason for this

is that the beamwidth of the antenna determines the angular resolution of a radar. A smaller

HPBW gives better angular resolution. The radar will be better able to separate close targets

in the angular dimension.

A-14

A.3 Microwave theory

In this section some important topics from microwave theory are presented. First a brief

description is given of general transmission lines. Then S-parameters and the Smith chart are

presented. S-parameters and the Smith chart are useful tools and have been used excessively

in the design of the antenna.

Transmission lines

[5, pp. 47-50]

Transmission lines are important components in a RF-system. In general a transmission line

transfers energy from one point to another but it can also be used as a component in filters,

matching networks, and so on.

When the frequency is so high that the dimension of the circuit becomes a notable fraction of

the wavelength, the lumped circuit theory can no longer be used. Lumped circuit theory

assumes that the voltage over the length of a line is constant, but when the frequency is high

the amplitude and phase of the voltage will not be constant over the line. In this case

transmission line theory must be used to take into account the changing amplitude and phase

of the voltage along the line. It is this property (changing amplitude and phase as a function of

z, where z is the position on the line) that makes it possible to use a transmission line as a

circuit component.

The equations that describe the traveling wave along a line are

(A.10)

(A.11)

where and

are the voltage amplitudes in respectively positive and negative z direction,

and

are the current amplitudes, describes propagation in positive z direction, and

describes propagation in negative direction.

(A.12)

is the propagation constant, is the attenuation constant and models the loss in the

transmission line, and is the phase constant.

A-15

Characteristic impedance

[5, p. 50]

The characteristic impedance of a transmission line is defined as the ratio of the voltage

amplitude to the current amplitude

(A.13)

The characteristic impedance is constant over the entire length of the transmission line as long

as the geometry of the line does not change [4, p. 440].

Terminated transmission line

[5, pp. 56-62]

When a transmission line is terminated in a load, as shown in Figure 60 and , some

portion of the wave will be reflected by the load.

Figure 60: Terminated transmission line

This is because the ratio of the voltage to the current at the terminal is different from the

voltage to current ratio on the line since

(A.14)

This means that a part of the incoming wave has to be reflected. A measure of the reflection is

the reflection coefficient, defined by

(A.15)

When the incident wave and reflected wave combine on the transmission line a standing wave

is formed. The voltage standing wave ratio (VSWR) is defined as

A-16

(A.16)

and gives the ratio of the maximum voltage amplitude to the minimum voltage amplitude on

the transmission line.

S-parameters

[5, pp. 178-179]

S-parameters or the scattering matrix is a standard method for describing microwave

networks. It uses voltage waves, both incident, ,and reflected, to determine the

properties of a microwave network. An advantage S-parameters have over other similar

methods is that it is easier to measure incident and reflected voltage waves at high frequencies

than actual voltages and currents on the terminal.

A two port network is shown in Figure 61.

Figure 61: Two port network

This network can be described by the scattering matrix [5, p. 178]

(A.17)

here and

are the reflected voltage waves from respectively port 1 and port 2, and

and are the incident voltage waves on port 1 and port 2. From (A.17) a generalized

equation to determine the S-parameters is found

(A.18)

A-17

To determine for a N port network one has to excite only port j and then measure at port i,

the ports need to be terminated in a match so nothing is reflected back into the network. is

the transmission coefficient from port j to port i. is the reflection coefficient at port i. This

means that the input impedance at port 1 can be determined from since

(A.19)

The patch antenna in this project is modeled as a one-port network. This means that the only

S-parameter is . is an important parameter since it describes the input impedance of the

antenna which is the main limiter on the bandwidth.

Smith chart

[5, pp. 63-67]

A very useful tool is the Smith chart, which is a graphical tool showing the reflection

coefficient or normalized impedances. It is used for matching of circuits.

The Smith chart is a polar plot of the reflection coefficient = . The is the radius

plotted from the center of the Smith chart and is the phase and is plotted from right to left

( ). Dividing by the characteristic impedance the reflection coefficient can

be written as

(A.20)

where is the normalized load impedance. can be solved from (A.20)

(A.21)

This means that the Smith chart can be used to convert the voltage reflection coefficient to

the normalized load impedance. The resistance part of is plotted along the horizontal

circles and the reactance of is plotted on the vertical circles.

The reflection coefficient can be plotted over a range of frequencies in the Smith chart. This

gives a good description of the input impedance.

A-18

Dielectric Substrates

An important part of the patch antenna is the dielectric substrate. The substrate properties

have a large effect on the patch antenna. It is not just a mechanical object that holds the

antenna together and makes it practical to produce. Its electrical and thermal properties are

important to consider when a desired antenna specification is to be achieved.

Electric properties

Materials can be divided into three different groups according to their electrical properties;

conductors, semiconductors and insulators. A dielectric substrate belongs to the latter

category. This means that it will not lead any electrical current [4, p. 101]. An insulator can be

described by its electric permittivity and magnetic permeability which is defined below for a

linear and isotropic insulator;

(A.22)

(A.23)

and is the permittivity and permeability in vacuum. is

the relative permeability and it describes how a material reacts to a magnetic field. For

materials considered in this report . The permeability of the material will therefore not

be considered further in this report.

The most common parameter used to describe a dielectric substrate is . It is called the

relative permittivity or the dielectric constant. Due to the polarization that occurs inside an

insulator when a electric field is applied on the outside of the material, the electric field

strength inside the insulator will be weaker than what it would be in vacuum [4, p. 109]. The

dielectric constant is related to this effect and therefore describes how the material reacts to an

electric field. A high dielectric constant means that strong polarization occurs, which in turn

means that the field inside the material is weaker [4, pp. 109-110]. One can say that a material

with high dielectric constant stores energy better than a material with low dielectric constant.

Another important parameter used to describe a material is the loss tangent defined as

(A.24)

where is the conductivity of the material and is the frequency [4, p. 342]. The loss

tangent describes the power loss in the material. It takes into account both losses due to

polarization of the material and ohmic losses [4, p. 342]. It is important to have the loss

tangent as low as possible to achieve good antenna efficiency.

Thermal properties

The thermal properties of the substrate are important to consider, specifically when the

substrate is used in high power applications. Some of the energy applied to a circuit will be

A-19

dissipated as heat. This is due to the loss in the substrate, the finite conductivity of the

conductor and electronic components, such as power amplifiers with low efficiencies. One

way to decrease the temperature rise is to etch the circuit on a substrate with good thermal

properties. Which parameters to consider for good thermal design are presented below.

To minimize the amount of energy dissipated as heat one can reduce the loss in the substrate.

This makes the loss tangent a good indicator of the substrates thermal properties. A low loss

tangent means that less energy is dissipated as heat due to the losses in the substrate.

Thermal conductivity is another parameter that affects the thermal properties of the substrate.

The thermal conductivity describes how good the substrate is to transfer heat. A substrate with

high thermal conductivity will cool down quicker than a substrate with low thermal

conductivity [24].

Other parameters to consider are the thermal coefficient of the dielectric constant and

coefficient of thermal expansion. Atoms in the substrate will behave differently at different

temperatures, this can lead to changes in the dielectric constant. The thermal coefficient of the

dielectric constant describes how much the dielectric constant will change when the

temperature changes. If this is high the antennas properties will vary at different temperatures.

The coefficient of thermal expansion describes how much the dimensions of the substrate will

change when the temperature changes.

B-1

Appendix B: Measurements

B.1 Input impedance

To measure the reflection coefficient a network analyzer was used. Network analyzer was

calibrated for a frequency band of 7-10 GHz. Then measurements were conducted. Figure 62

and Figure 63 shows the reflection coefficients of the original antenna element.

Original antenna element

Figure 62: S11 plotted in a Smith chart for a frequency band of 7-10 GHz (a) Antenna 3, (b) Antenna 4, (c)

Antenna 5

B-2

Figure 63: S11 plotted in dB as a function of frequency (a) Antenna 3, (b) Antenna 4, (c) Antenna 5

It is seen in Figure 62 that the loop due to the coupling between the patches is missing. This

has led to the center frequency being moved to 8 GHz and the bandwidth is much lower than

expected as seen in Figure 63. Comparing the results only small deviations between the

antennas are observed. This indicates small process variations.

B-3

Modified antenna element

Figure 64: S11of the modified antenna element plotted in a Smith chart for a frequency band of 7-10 GHz

(a) Antenna 3, (b) Antenna 4, (c) Antenna 5

B-4

Figure 65: S11 of the modified antenna element plotted in dB as a function of frequency (a) Antenna 3, (b)

Antenna 4, (c) Antenna 5

It is seen from Figure 64 that the loop is missing for the modified antenna element. This

antenna has a very good match only at the wrong center frequency.

B-5

B.2 Radiation patterns

To measure the radiation pattern of the antenna an anechoic chamber was used. The test setup

is shown in Figure 66. The antenna under test (AUT) is mounted on a rotating stand across

from a reference antenna. This test setup measures the transmission coefficient S21 by

exciting the reference antenna and then measuring the power received by the AUT. The AUT

is rotated 360°.

Figure 66: Anechoic chamber

The reference antenna is a broadband horn with linear polarization. This makes it possible to

measure both E-plane, H-plane and cross polarization only by turning the reference antenna.

measurements was conducted for three frequencies; 8, 8,25 and 8,50 GHz. A sample of the

measured results are presented here. The results are plotted in normalized dB.

B-6

Original antenna element

Figure 67: Antenna 4 at 8.25 GHz in normalized dB, (a) E-plane, (b) H-plane

Figure 68: Antenna 3 at 8.5 GHz in normalized dB, (a) E-plane, (b) H-plane

B-7

Figure 69: Radiation pattern for the Antenna 3 at 8.5 GHz in normalized dB, (a) E-plane, (b) H-plane

Figure 70: Cross polarization for antenna 4 at 8.25 GHz

B-8

Modified antenna element

Figure 71: Radiation pattern for antenna 4 at 8.25 GHz in normalized dB, (a) E-plane, (b) H-plane

Figure 72: Radiation pattern for antenna 5 at 8.25 GHz in normalized dB, (a) E-plane, (b) H-plane

B-9

Figure 73: Cross polarization of antenna 5 at 8.25 GHz

C-1

Appendix C: Simulation results

C.1 Radiation patterns

Figure 74: Rectangular plot of the normalized antenna gain in dB for the array scanned in (f=

8.25 GHz). Plotted in plane.


8.25 GHz). Plotted in φ=0° plane.

C-2


8.25 GHz). Plotted in φ=0° plane.

Figure 77: Rectangular plot of the normalized antenna gain in dB for the array scanned in and

(f= 8.25 GHz). Plotted in φ=45° plane.

C-3

Figure 78: Rectangular plot of the normalized antenna gain in dB for the array scanned in and


Figure 79: Polar plot of the normalized antenna gain in dB for the array scanned in and


C-4

Figure 80: Rectangular plot of the normalized antenna gain in dB for an antenna element in an infinite

array environment. φ=0°

Figure 81: Rectangular plot of the normalized antenna gain in dB for an antenna element in an infinite

array environment. φ=90°

:

D-1

Appendix D: Schematic

Table 10: Values for the schematic

Parameter Value [mm]

L 16.5

W 16.5

L1 8

W1 7.5

L2 10.5

W2 8

Ls 9.5

L_st 2.8

W_st 2.8

L_sl 4.5

W_sl 0.5

L_c 6.3

W_c 11

R_t 1.5

R1 0.2

R2 0.3

R3 0.635

d1 1.1

d2 0.7

Copper thickness

D-2

Figure 82: Side view of antenna

D-3

Figure 83: Schematics of the antenna element

D-4

Figure 84: Cage and RF-Transition. Red vias go from ground shield to feed layer. White vias go from

ground shield to ground plane

.

D-5

Figure 85: Schematic of the array

E-1

Appendix E: Derivations The propagation direction relative to the z-axis for a Floquet mode is given as [2, p. 73]

(E.1)

where is the phase difference and d is the element spacing. Multiple steps are taken to

simplify this equation.

(E.2)

(E.3)

(E.4)

Inserting

for .

(E.5)

Then is used

(E.6)

Solving with respect to gives

(E.7)

(E.8)

(E.9)

Design and Analysis of an X-band Phased Array Patch Antenna · The array has achieved a half power...

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